Explore · MATH-5B-C15-L06-OPEN
A price starts at $220 and rises 15%. Find its new price.
Great Inheritance Mathematics Term B · Original independent course
Word Problems
Watch for: Reversing percentage change bases or adding percentages to units.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C15-L06-PREREQ
An item is $100 before a 10% increase. What is the new price?
Show worked answer (after attempting)
Answer: $110
10% of 100 is $10; add it to $100 for $110.
Understand the idea
Solve percentage problems for part, whole and changed amount with explicit base quantities. The essential earlier idea is: Chapter 15 L01–05, ratios and decimal multiplication.. The model below will always use the actual quantities from the worked problem. Check reversing percentage change bases or adding percentages to units when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C15-L06-Q01
A price starts at $200 and rises 15%. Find its new price.
Solution: $230
Base is the original 200. Change = 15/100 × 200 = 30; then add to obtain 230.
Worked example 2 · MATH-5B-C15-L06-Q02
A fee of $160 is reduced by 25%. Find the amount left.
Solution: $120
Base is the original 160. Change = 25/100 × 160 = 40; then subtract to obtain 120.
Worked example 3 · MATH-5B-C15-L06-Q03
A quantity begins at 120 and increases 40%. Find the change and final amount.
Solution: change 48; final 168
Base is the original 120. Change = 40/100 × 120 = 48; then add to obtain 168.
Check understanding
1 · MATH-5B-C15-L06-Q04
A price starts at $220 and rises 15%. Find its new price.
Show worked answer (after attempting)
Answer: $253
Base is the original 220. Change = 15/100 × 220 = 33; then add to obtain 253.
2 · MATH-5B-C15-L06-Q05
A fee of $180 is reduced by 25%. Find the amount left.
Show worked answer (after attempting)
Answer: $135
Base is the original 180. Change = 25/100 × 180 = 45; then subtract to obtain 135.
3 · MATH-5B-C15-L06-Q06
A quantity begins at 140 and increases 40%. Find the change and final amount.
Show worked answer (after attempting)
Answer: change 56; final 196
Base is the original 140. Change = 40/100 × 140 = 56; then add to obtain 196.
Guided practice
1 · MATH-5B-C15-L06-Q07
A price starts at $240 and rises 15%. Find its new price.
Show worked answer (after attempting)
Answer: $276
Base is the original 240. Change = 15/100 × 240 = 36; then add to obtain 276.
2 · MATH-5B-C15-L06-Q08
A fee of $200 is reduced by 25%. Find the amount left.
Show worked answer (after attempting)
Answer: $150
Base is the original 200. Change = 25/100 × 200 = 50; then subtract to obtain 150.
3 · MATH-5B-C15-L06-Q09
A quantity begins at 160 and increases 40%. Find the change and final amount.
Show worked answer (after attempting)
Answer: change 64; final 224
Base is the original 160. Change = 40/100 × 160 = 64; then add to obtain 224.
4 · MATH-5B-C15-L06-Q10
A price starts at $260 and rises 15%. Find its new price.
Show worked answer (after attempting)
Answer: $299
Base is the original 260. Change = 15/100 × 260 = 39; then add to obtain 299.
Independent practice
1 · MATH-5B-C15-L06-Q11
A fee of $220 is reduced by 25%. Find the amount left.
Show worked answer (after attempting)
Answer: $165
Base is the original 220. Change = 25/100 × 220 = 55; then subtract to obtain 165.
2 · MATH-5B-C15-L06-Q12
A quantity begins at 180 and increases 40%. Find the change and final amount.
Show worked answer (after attempting)
Answer: change 72; final 252
Base is the original 180. Change = 40/100 × 180 = 72; then add to obtain 252.
3 · MATH-5B-C15-L06-Q13
A price starts at $280 and rises 15%. Find its new price.
Show worked answer (after attempting)
Answer: $322
Base is the original 280. Change = 15/100 × 280 = 42; then add to obtain 322.
4 · MATH-5B-C15-L06-Q14
A fee of $240 is reduced by 25%. Find the amount left.
Show worked answer (after attempting)
Answer: $180
Base is the original 240. Change = 25/100 × 240 = 60; then subtract to obtain 180.
5 · MATH-5B-C15-L06-Q15
A quantity begins at 200 and increases 40%. Find the change and final amount.
Show worked answer (after attempting)
Answer: change 80; final 280
Base is the original 200. Change = 40/100 × 200 = 80; then add to obtain 280.
6 · MATH-5B-C15-L06-Q16
A price starts at $300 and rises 15%. Find its new price.
Show worked answer (after attempting)
Answer: $345
Base is the original 300. Change = 15/100 × 300 = 45; then add to obtain 345.
7 · MATH-5B-C15-L06-Q17
A fee of $260 is reduced by 25%. Find the amount left.
Show worked answer (after attempting)
Answer: $195
Base is the original 260. Change = 25/100 × 260 = 65; then subtract to obtain 195.
8 · MATH-5B-C15-L06-Q18
A quantity begins at 220 and increases 40%. Find the change and final amount.
Show worked answer (after attempting)
Answer: change 88; final 308
Base is the original 220. Change = 40/100 × 220 = 88; then add to obtain 308.
Challenge and error analysis
1 · MATH-5B-C15-L06-ERR1
The assigned question is: “A fee of $320 is reduced by 25%. Find the amount left.” A learner wrote: “I used the final value, not the original base involving 320, in the percentage calculation and wrote $240.1.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: $240
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: $240. Recompute from the given data: Base is the original 320. Change = 25/100 × 320 = 80; then subtract to obtain 240.
2 · MATH-5B-C15-L06-ERR2
The assigned question is: “A quantity begins at 280 and increases 40%. Find the change and final amount.” A learner wrote: “I used the final value, not the original base involving 280, in the percentage calculation and wrote change 113; final 392.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: change 112; final 392
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: change 112; final 392. Recompute from the given data: Base is the original 280. Change = 40/100 × 280 = 112; then add to obtain 392.
Exit check
Exit · MATH-5B-C15-L06-Q19
A price starts at $320 and rises 15%. Find its new price.
Show worked answer (after attempting)
Answer: $368
Base is the original 320. Change = 15/100 × 320 = 48; then add to obtain 368.