Ratios and Proportional Relationships: Solving Multistep Ratio and Percent Problems (CCSS.7.RP.3)
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Common Core 7th Grade Math › Ratios and Proportional Relationships: Solving Multistep Ratio and Percent Problems (CCSS.7.RP.3)
A group's meal costs 52 dollars before tip. They leave a 15% tip and split the total evenly among 4 people. How much does each person pay?
\$14.95
\$13.00
\$16.75
\$59.80
Explanation
Step 1: Tip: $52 \times 0.15 = 7.80$. Step 2: Total with tip: $52 + 7.80 = 59.80$. Step 3: Per person: $59.80 \div 4 = 14.95$. Why others are wrong: B) $52 \div 4 = 13$ forgot to include the tip. C) Treated 15% as 15 dollars: $(52 + 15) \div 4 = 16.75$. D) Forgot to split the bill after adding tip.
A pizza bill is 32 dollars. A coupon takes 25% off the price. After the discount, they leave a 20% tip on the discounted price. What is the total amount paid, in dollars?
\$24.00
\$30.40
\$46.40
\$28.80
Explanation
Discount: $0.25 \times 32 = 8$, so discounted price is $32 - 8 = 24$. Tip: $0.20 \times 24 = 4.80$. Total: $24 + 4.80 = 28.80$. A: 24.00 forgets the tip. B: 30.40 tips on the original price ($0.20\times32=6.40$) instead of the discounted price. C: 46.40 adds the discount instead of subtracting and also tips on the original ($32 + 8 + 6.40$).
A hoodie has an original price of 48 dollars. It is discounted 25%, and then an 8% sales tax is applied to the discounted price. What is the final price, in dollars, to the nearest cent?
\$36.00
\$38.88
\$51.84
\$39.84
Explanation
Discount: $0.25 \times 48 = 12$, so discounted price is $48 - 12 = 36$. Tax: $0.08 \times 36 = 2.88$. Final price: $36 + 2.88 = 38.88$. A: 36.00 stops before adding tax. C: 51.84 ignores the discount and taxes the original ($48 + 0.08\times48$). D: 39.84 applies tax to the original instead of the discounted price ($36 + 0.08\times48$).
A store marks up a backpack by 25% from its cost of 36 dollars, then applies a 15% coupon to the marked price. What is the sale price before tax, in dollars?
\$39.60
\$45.00
\$30.00
\$38.25
Explanation
Marked price: $36 \times 1.25 = 45$. Coupon: $45 \times 0.15 = 6.75$. Sale price: $45 - 6.75 = 38.25$. A (39.60): applied the 15% to the cost or combined the percentages as $36 \times 1.10$ (incorrect). B (45.00): forgot to apply the coupon. C (30.00): subtracted 15 dollars instead of 15% of the marked price.
A jacket costs 60 dollars. It is 25% off, and then an 8% sales tax is applied to the discounted price. What is the total price you pay?
\$40.20
\$64.80
\$48.60
\$49.80
Explanation
Step 1: Find the discount: $60 \times 0.25 = 15$. Sale price: $60 - 15 = 45$. Step 2: Find tax on the sale price: $45 \times 0.08 = 3.60$. Step 3: Total: $45 + 3.60 = 48.60$. Why others are wrong: A) Treated discount and tax as one combined percent: $60 \times (1 - (0.25 + 0.08)) = 40.20$. B) Forgot the discount and just taxed the original: $60 \times 1.08 = 64.80$. D) Used the correct discounted price but computed tax on the original: $45 + (60 \times 0.08) = 49.80$.
A restaurant bill is 48 dollars before tax. The tip is 18% of the pre-tax amount, and sales tax is 8%. What is the total amount paid, in dollars?
\$60.48
\$61.17
\$51.84
\$69.84
Explanation
Tip: $48 \times 0.18 = 8.64$. Tax: $48 \times 0.08 = 3.84$. Total: $48 + 8.64 + 3.84 = 60.48$. B (61.17): calculated the tip on the taxed total $(48 + 3.84)$ instead of on 48. C (51.84): added tax but forgot the tip. D (69.84): treated 18% as 18 dollars and added it.
Jamie earns a base pay of 50 dollars per day plus 6% commission on sales. One day she sells 350 dollars worth of items and pays a 10 dollar booth fee from her earnings. How much does she take home that day?
\$61.00
\$71.00
\$42.10
\$250.00
Explanation
Commission: $350 \times 0.06 = 21$. Add base pay: $50 + 21 = 71$. Subtract fee: $71 - 10 = 61$. Why others: 71.00 forgets to subtract the booth fee. 42.10 comes from a decimal mistake computing commission as \$2.10$ (using \$0.006$) before subtracting the fee. 250.00 uses 60% instead of 6%: $350 \times 0.60 = 210$, then $50 - 10 + 210 = 250$, which is incorrect.
A jacket costs 60 dollars. It is on sale for 25% off. After the discount, 8% sales tax is added. What is the final price?
\$64.80
\$45.00
\$49.80
\$48.60
Explanation
Discount: $60 \times 0.25 = 15$. Discounted price: $60 - 15 = 45$. Tax on discounted price: $45 \times 0.08 = 3.60$. Final price: $45 + 3.60 = 48.60$. Why others: 64.80 adds 8% tax to the original price ($60 \times 1.08$) and ignores the discount. 45.00 subtracts the discount but forgets to add tax. 49.80 applies the discount after tax: $60 \times 1.08 = 64.80$ then $64.80 - 15 = 49.80$, which is the wrong order.
A jacket costs 80 dollars. It is discounted by 25%, then a 7% sales tax is applied to the discounted price. What is the final price, in dollars?
\$65.60
\$85.60
\$64.20
\$60.00
Explanation
Discount: $80 \times 0.25 = 20$, so discounted price is $80 - 20 = 60$. Tax: $60 \times 0.07 = 4.20$. Final price: $60 + 4.20 = 64.20$. A (65.60): used $80 \times (1 - 0.25 + 0.07)$ or mixed the order, effectively taxing the original. B (85.60): forgot the discount and taxed the original $80$. D (60.00): forgot to add tax.
A savings account earns simple interest at 4% per year. If 600 dollars is deposited and left for 3 years, what is the total amount in the account after 3 years, in dollars?
\$72.00
\$624.00
\$672.00
\$1,320.00
Explanation
Simple interest: $I = P r t = 600 \times 0.04 \times 3 = 72$. Total amount: $600 + 72 = 672$. A: 72.00 is the interest only, not the total. B: 624.00 multiplies by the rate once ($600\times0.04=24$) and forgets the time factor. D: 1320.00 uses 40% instead of 4% (\$0.4$ instead of \$0.04$).