Reference / Curriculum / 3B / Chapter 15

3B · Chapter 15 · Solutions

Complete worked answer key

Answers and explanations for every original lesson practice set and chapter assessment.

Print this separately from student practice sheets. These are public worked solutions, not secure examination materials.

Dollars and Cents

Prerequisite

100 — One dollar is exactly 100 cents. Ten groups of ten cents, or four quarters of 25 cents each, both total 100 cents.
950 — Seven hundreds plus two hundreds and five tens.
650 — Subtract in hundreds and tens or use regrouping.

Understanding checks

$5.69 — There are 100 cents in one dollar; 569 cents = 5 dollars and 69 cents.
$7.82 — There are 100 cents in one dollar; 782 cents = 7 dollars and 82 cents.
$4.17 — There are 100 cents in one dollar; 417 cents = 4 dollars and 17 cents.

Guided

$3.28 — There are 100 cents in one dollar; 328 cents = 3 dollars and 28 cents.
$1.63 — There are 100 cents in one dollar; 163 cents = 1 dollar and 63 cents.
$5.84 — There are 100 cents in one dollar; 584 cents = 5 dollars and 84 cents.
$2.21 — There are 100 cents in one dollar; 221 cents = 2 dollars and 21 cents.
$2.07 — There are 100 cents in one dollar; 207 cents = 2 dollars and 7 cents.

Independent

$2.28 — There are 100 cents in one dollar; 228 cents = 2 dollars and 28 cents.
$7.25 — There are 100 cents in one dollar; 725 cents = 7 dollars and 25 cents.
$7.54 — There are 100 cents in one dollar; 754 cents = 7 dollars and 54 cents.
$5.83 — There are 100 cents in one dollar; 583 cents = 5 dollars and 83 cents.
$3.10 — There are 100 cents in one dollar; 310 cents = 3 dollars and 10 cents.
$6.94 — There are 100 cents in one dollar; 694 cents = 6 dollars and 94 cents.
$8.01 — There are 100 cents in one dollar; 801 cents = 8 dollars and 1 cents.
$2.59 — There are 100 cents in one dollar; 259 cents = 2 dollars and 59 cents.

Challenge

$3.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.
$6.25 — Count 25 cents to $4.00, then $6.00 more to $10.00, for $6.25 change.

Exit

$8.30 — There are 100 cents in one dollar; 830 cents = 8 dollars and 30 cents.
$4.82 — There are 100 cents in one dollar; 482 cents = 4 dollars and 82 cents.
$6.10 — There are 100 cents in one dollar; 610 cents = 6 dollars and 10 cents.

Making $10

Prerequisite

$8.67 — There are 100 cents in one dollar; 867 cents = 8 dollars and 67 cents.
$8.37 — There are 100 cents in one dollar; 837 cents = 8 dollars and 37 cents.
$3.80 — There are 100 cents in one dollar; 380 cents = 3 dollars and 80 cents.

Understanding checks

$8.73 — 10 dollars is 1,000 cents. Subtract 127 cents to get 873 cents, or $8.73.
$4.88 — 10 dollars is 1,000 cents. Subtract 512 cents to get 488 cents, or $4.88.
$4.92 — 10 dollars is 1,000 cents. Subtract 508 cents to get 492 cents, or $4.92.

Guided

$1.71 — 10 dollars is 1,000 cents. Subtract 829 cents to get 171 cents, or $1.71.
$8.28 — 10 dollars is 1,000 cents. Subtract 172 cents to get 828 cents, or $8.28.
$5.07 — 10 dollars is 1,000 cents. Subtract 493 cents to get 507 cents, or $5.07.
$7.87 — 10 dollars is 1,000 cents. Subtract 213 cents to get 787 cents, or $7.87.
$1.81 — 10 dollars is 1,000 cents. Subtract 819 cents to get 181 cents, or $1.81.

Independent

$6.56 — 10 dollars is 1,000 cents. Subtract 344 cents to get 656 cents, or $6.56.
$1.60 — 10 dollars is 1,000 cents. Subtract 840 cents to get 160 cents, or $1.60.
$4.32 — 10 dollars is 1,000 cents. Subtract 568 cents to get 432 cents, or $4.32.
$6.44 — 10 dollars is 1,000 cents. Subtract 356 cents to get 644 cents, or $6.44.
$8.11 — 10 dollars is 1,000 cents. Subtract 189 cents to get 811 cents, or $8.11.
$6.15 — 10 dollars is 1,000 cents. Subtract 385 cents to get 615 cents, or $6.15.
$3.42 — 10 dollars is 1,000 cents. Subtract 658 cents to get 342 cents, or $3.42.
$2.52 — 10 dollars is 1,000 cents. Subtract 748 cents to get 252 cents, or $2.52.

Challenge

$4.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.
$5.25 — Count 25 cents to $5.00, then $5.00 more to $10.00, for $5.25 change.

Exit

$6.36 — 10 dollars is 1,000 cents. Subtract 364 cents to get 636 cents, or $6.36.
$7.26 — 10 dollars is 1,000 cents. Subtract 274 cents to get 726 cents, or $7.26.
$1.34 — 10 dollars is 1,000 cents. Subtract 866 cents to get 134 cents, or $1.34.

Adding Money

Prerequisite

$7.24 — 10 dollars is 1,000 cents. Subtract 276 cents to get 724 cents, or $7.24.
$4.51 — 10 dollars is 1,000 cents. Subtract 549 cents to get 451 cents, or $4.51.
$4.26 — 10 dollars is 1,000 cents. Subtract 574 cents to get 426 cents, or $4.26.

Understanding checks

$11.44 — Add cents: 833 + 311 = 1144 cents = $11.44.
$9.37 — Add cents: 680 + 257 = 937 cents = $9.37.
$2.33 — Add cents: 145 + 88 = 233 cents = $2.33.

Guided

$4.15 — Add cents: 159 + 256 = 415 cents = $4.15.
$6.97 — Add cents: 468 + 229 = 697 cents = $6.97.
$8.54 — Add cents: 660 + 194 = 854 cents = $8.54.
$8.10 — Add cents: 696 + 114 = 810 cents = $8.10.
$6.51 — Add cents: 271 + 380 = 651 cents = $6.51.

Independent

$6.24 — Add cents: 392 + 232 = 624 cents = $6.24.
$10.06 — Add cents: 666 + 340 = 1006 cents = $10.06.
$10.49 — Add cents: 703 + 346 = 1049 cents = $10.49.
$9.03 — Add cents: 622 + 281 = 903 cents = $9.03.
$11.55 — Add cents: 859 + 296 = 1155 cents = $11.55.
$10.02 — Add cents: 649 + 353 = 1002 cents = $10.02.
$7.23 — Add cents: 624 + 99 = 723 cents = $7.23.
$6.42 — Add cents: 350 + 292 = 642 cents = $6.42.

Challenge

$5.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.
$4.25 — Count 25 cents to $6.00, then $4.00 more to $10.00, for $4.25 change.

Exit

$6.08 — Add cents: 445 + 163 = 608 cents = $6.08.
$7.29 — Add cents: 622 + 107 = 729 cents = $7.29.
$8.89 — Add cents: 603 + 286 = 889 cents = $8.89.

Subtracting Money

Prerequisite

$8.89 — Add cents: 538 + 351 = 889 cents = $8.89.
$10.07 — Add cents: 843 + 164 = 1007 cents = $10.07.
$5.49 — Add cents: 261 + 288 = 549 cents = $5.49.

Understanding checks

$1.30 — Subtract 88 cents from 218 cents. The 130 cents remaining equal $1.30.
$8.42 — Subtract 96 cents from 938 cents. The 842 cents remaining equal $8.42.
$7.55 — Subtract 380 cents from 1135 cents. The 755 cents remaining equal $7.55.

Guided

$3.28 — Subtract 165 cents from 493 cents. The 328 cents remaining equal $3.28.
$8.11 — Subtract 71 cents from 882 cents. The 811 cents remaining equal $8.11.
$6.05 — Subtract 238 cents from 843 cents. The 605 cents remaining equal $6.05.
$5.57 — Subtract 360 cents from 917 cents. The 557 cents remaining equal $5.57.
$3.97 — Subtract 134 cents from 531 cents. The 397 cents remaining equal $3.97.

Independent

$5.36 — Subtract 273 cents from 809 cents. The 536 cents remaining equal $5.36.
$2.92 — Subtract 249 cents from 541 cents. The 292 cents remaining equal $2.92.
$5.70 — Subtract 214 cents from 784 cents. The 570 cents remaining equal $5.70.
$8.62 — Subtract 212 cents from 1074 cents. The 862 cents remaining equal $8.62.
$3.78 — Subtract 132 cents from 510 cents. The 378 cents remaining equal $3.78.
$5.35 — Subtract 157 cents from 692 cents. The 535 cents remaining equal $5.35.
$7.95 — Subtract 287 cents from 1082 cents. The 795 cents remaining equal $7.95.
$3.60 — Subtract 187 cents from 547 cents. The 360 cents remaining equal $3.60.

Challenge

$6.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.
$3.25 — Count 25 cents to $7.00, then $3.00 more to $10.00, for $3.25 change.

Exit

$6.41 — Subtract 328 cents from 969 cents. The 641 cents remaining equal $6.41.
$4.79 — Subtract 180 cents from 659 cents. The 479 cents remaining equal $4.79.
$7.66 — Subtract 202 cents from 968 cents. The 766 cents remaining equal $7.66.

Word Problems

Prerequisite

$8.42 — Subtract 269 cents from 1111 cents. The 842 cents remaining equal $8.42.
$7.94 — Subtract 293 cents from 1087 cents. The 794 cents remaining equal $7.94.
$7.91 — Subtract 327 cents from 1118 cents. The 791 cents remaining equal $7.91.

Understanding checks

$15.66 — Combine the costs: $1.28 + $3.06 = $4.34. Then subtract from $20.00 to get $15.66.
$21.77 — Combine the costs: $5.99 + $2.24 = $8.23. Then subtract from $30.00 to get $21.77.
$24.41 — Combine the costs: $3.29 + $2.30 = $5.59. Then subtract from $30.00 to get $24.41.

Guided

$23.60 — Combine the costs: $5.46 + $0.94 = $6.40. Then subtract from $30.00 to get $23.60.
$13.05 — Combine the costs: $6.24 + $0.71 = $6.95. Then subtract from $20.00 to get $13.05.
$9.38 — Combine the costs: $8.68 + $1.94 = $10.62. Then subtract from $20.00 to get $9.38.
$25.39 — Combine the costs: $2.36 + $2.25 = $4.61. Then subtract from $30.00 to get $25.39.
$24.59 — Combine the costs: $4.00 + $1.41 = $5.41. Then subtract from $30.00 to get $24.59.

Independent

$19.92 — Combine the costs: $7.20 + $2.88 = $10.08. Then subtract from $30.00 to get $19.92.
$21.64 — Combine the costs: $5.77 + $2.59 = $8.36. Then subtract from $30.00 to get $21.64.
$22.54 — Combine the costs: $6.22 + $1.24 = $7.46. Then subtract from $30.00 to get $22.54.
$23.27 — Combine the costs: $4.91 + $1.82 = $6.73. Then subtract from $30.00 to get $23.27.
$13.78 — Combine the costs: $5.09 + $1.13 = $6.22. Then subtract from $20.00 to get $13.78.
$9.60 — Combine the costs: $6.60 + $3.80 = $10.40. Then subtract from $20.00 to get $9.60.
$15.81 — Combine the costs: $2.12 + $2.07 = $4.19. Then subtract from $20.00 to get $15.81.
$20.87 — Combine the costs: $5.77 + $3.36 = $9.13. Then subtract from $30.00 to get $20.87.

Challenge

$7.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.
$2.25 — Count 25 cents to $8.00, then $2.00 more to $10.00, for $2.25 change.

Exit

$25.88 — Combine the costs: $1.64 + $2.48 = $4.12. Then subtract from $30.00 to get $25.88.
$22.86 — Combine the costs: $6.41 + $0.73 = $7.14. Then subtract from $30.00 to get $22.86.
$24.02 — Combine the costs: $3.57 + $2.41 = $5.98. Then subtract from $30.00 to get $24.02.

Practice

$5.28 — There are 100 cents in one dollar; 528 cents = 5 dollars and 28 cents.
$6.39 — 10 dollars is 1,000 cents. Subtract 361 cents to get 639 cents, or $6.39.
$7.06 — Add cents: 393 + 313 = 706 cents = $7.06.
$6.37 — Subtract 144 cents from 781 cents. The 637 cents remaining equal $6.37.
$9.74 — Combine the costs: $6.59 + $3.67 = $10.26. Then subtract from $20.00 to get $9.74.
$7.64 — There are 100 cents in one dollar; 764 cents = 7 dollars and 64 cents.
$1.82 — 10 dollars is 1,000 cents. Subtract 818 cents to get 182 cents, or $1.82.
$6.27 — Add cents: 346 + 281 = 627 cents = $6.27.
$6.97 — Subtract 89 cents from 786 cents. The 697 cents remaining equal $6.97.
$26.91 — Combine the costs: $1.36 + $1.73 = $3.09. Then subtract from $30.00 to get $26.91.
$2.71 — There are 100 cents in one dollar; 271 cents = 2 dollars and 71 cents.
$7.68 — 10 dollars is 1,000 cents. Subtract 232 cents to get 768 cents, or $7.68.
$3.85 — Add cents: 159 + 226 = 385 cents = $3.85.
$2.70 — Subtract 116 cents from 386 cents. The 270 cents remaining equal $2.70.
$26.34 — Combine the costs: $1.58 + $2.08 = $3.66. Then subtract from $30.00 to get $26.34.
$4.42 — There are 100 cents in one dollar; 442 cents = 4 dollars and 42 cents.
$2.25 — Count 25 cents to $8.00, then $2.00 more to $10.00, for $2.25 change.
$6.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.

Chapter Review

$1.21 — There are 100 cents in one dollar; 121 cents = 1 dollar and 21 cents.
$5.58 — 10 dollars is 1,000 cents. Subtract 442 cents to get 558 cents, or $5.58.
$11.04 — Add cents: 814 + 290 = 1104 cents = $11.04.
$2.31 — Subtract 371 cents from 602 cents. The 231 cents remaining equal $2.31.
$11.49 — Combine the costs: $5.49 + $3.02 = $8.51. Then subtract from $20.00 to get $11.49.
$2.97 — There are 100 cents in one dollar; 297 cents = 2 dollars and 97 cents.
$6.84 — 10 dollars is 1,000 cents. Subtract 316 cents to get 684 cents, or $6.84.
$6.56 — Add cents: 404 + 252 = 656 cents = $6.56.
$6.52 — Subtract 267 cents from 919 cents. The 652 cents remaining equal $6.52.
$20.84 — Combine the costs: $7.79 + $1.37 = $9.16. Then subtract from $30.00 to get $20.84.
$5.67 — There are 100 cents in one dollar; 567 cents = 5 dollars and 67 cents.
$6.50 — 10 dollars is 1,000 cents. Subtract 350 cents to get 650 cents, or $6.50.
$5.43 — Add cents: 186 + 357 = 543 cents = $5.43.
$1.24 — Subtract 83 cents from 207 cents. The 124 cents remaining equal $1.24.
$21.26 — Combine the costs: $7.15 + $1.59 = $8.74. Then subtract from $30.00 to get $21.26.
$3.94 — There are 100 cents in one dollar; 394 cents = 3 dollars and 94 cents.
$1.86 — 10 dollars is 1,000 cents. Subtract 814 cents to get 186 cents, or $1.86.
$7.07 — Add cents: 626 + 81 = 707 cents = $7.07.
$8.03 — Subtract 146 cents from 949 cents. The 803 cents remaining equal $8.03.
$16.92 — Combine the costs: $2.10 + $0.98 = $3.08. Then subtract from $20.00 to get $16.92.
$1.66 — There are 100 cents in one dollar; 166 cents = 1 dollar and 66 cents.
$8.55 — 10 dollars is 1,000 cents. Subtract 145 cents to get 855 cents, or $8.55.
$2.92 — Add cents: 119 + 173 = 292 cents = $2.92.
$3.06 — Subtract 337 cents from 643 cents. The 306 cents remaining equal $3.06.
$5.25 — Count 25 cents to $5.00, then $5.00 more to $10.00, for $5.25 change.
$3.05 — The first digit after the decimal is tens of cents, and the second is ones of cents.

Practice Exam

$4.27 — The suggested answer is not correct. Subtract 160 cents from 587 cents. The 427 cents remaining equal $4.27. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
$2.74 — There are 100 cents in one dollar; 274 cents = 2 dollars and 74 cents. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$4.69 — There are 100 cents in one dollar; 469 cents = 4 dollars and 69 cents. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$8.64 — 10 dollars is 1,000 cents. Subtract 136 cents to get 864 cents, or $8.64. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$9.64 — The suggested answer is not correct. Combine the costs: $7.13 + $3.23 = $10.36. Then subtract from $20.00 to get $9.64. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
$9.71 — Combine the costs: $8.59 + $1.70 = $10.29. Then subtract from $20.00 to get $9.71. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$9.80 — Add cents: 855 + 125 = 980 cents = $9.80. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$5.46 — Subtract 220 cents from 766 cents. The 546 cents remaining equal $5.46. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$8.00 — The suggested answer is not correct. There are 100 cents in one dollar; 800 cents = 8 dollars and 0 cents. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
$3.96 — Add cents: 315 + 81 = 396 cents = $3.96. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$9.61 — Add cents: 638 + 323 = 961 cents = $9.61. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$10.16 — Add cents: 652 + 364 = 1016 cents = $10.16. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$1.66 — The suggested answer is not correct. Subtract 360 cents from 526 cents. The 166 cents remaining equal $1.66. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
$5.87 — 10 dollars is 1,000 cents. Subtract 413 cents to get 587 cents, or $5.87. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$21.79 — Combine the costs: $4.69 + $3.52 = $8.21. Then subtract from $30.00 to get $21.79. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$5.15 — 10 dollars is 1,000 cents. Subtract 485 cents to get 515 cents, or $5.15. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$13.58 — The suggested answer is not correct. Combine the costs: $3.79 + $2.63 = $6.42. Then subtract from $20.00 to get $13.58. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
$4.26 — 10 dollars is 1,000 cents. Subtract 574 cents to get 426 cents, or $4.26. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$6.84 — Add cents: 475 + 209 = 684 cents = $6.84. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$1.45 — Subtract 142 cents from 287 cents. The 145 cents remaining equal $1.45. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$2.46 — The suggested answer is not correct. There are 100 cents in one dollar; 246 cents = 2 dollars and 46 cents. (3 points: 1 point for identifying the given answer as incorrect; 1 for explaining the error; 1 for giving the corrected solution and appropriate units.)
$8.28 — Subtract 141 cents from 969 cents. The 828 cents remaining equal $8.28. (2 points: 1 point for a mathematically valid calculation/model, 1 point for the correct final answer with units when appropriate.)
$6.25 — Count 25 cents to $4.00, then $6.00 more to $10.00, for $6.25 change. (3 points: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.)
$7.05 — The first digit after the decimal is tens of cents, and the second is ones of cents. (3 points: 1 point for the correct claim; 1 for a mathematical justification; 1 for a clear diagram, example, or relevant calculation when applicable.)