Full worked solutions for the 20 percent problems. Each answer shows the percent written as a decimal, the multiplication, the check, and the final amount in dollars. Compare every step with the worksheet work, especially the order of discount, tax and fees in the multistep problems.
Problem 1: Sales tax
Tax: \(0.07\times 28=1.96\). Total: \(28+1.96=29.96\).
Answer: tax $1.96; total $29.96.
Problem 2: Sales tax on a bike lock
Tax: \(0.06\times 24.50=1.47\). Total: \(24.50+1.47=25.97\). Check with the multiplier: \(24.50\times 1.06=25.97\).
Answer: tax $1.47; total $25.97.
Problem 3: Tip at a restaurant
Tip: \(0.20\times 36=7.2\). Total: \(36+7.2=43.2\). Check with the multiplier: \(36\times 1.20=43.2\).
Answer: tip $7.20; total $43.20.
Problem 4: Tip on a pizza order
Tip: \(0.15\times 42=6.3\). Total: \(42+6.3=48.3\). Check with the multiplier: \(42\times 1.15=48.3\).
Answer: tip $6.30; total $48.30.
Problem 5: Discount
Discount: \(0.25\times 64=16\). Sale price: \(64-16=48\). Check: \(64\times 0.75=48\).
Answer: discount $16; sale price $48.
Problem 6: Sale price of a tent
Discount: \(0.30\times 120=36\). Sale price: \(120-36=84\). Check: \(120\times 0.70=84\).
Answer: discount $36; sale price $84.
Problem 7: Markup
Markup: \(0.40\times 45=18\). Selling price: \(45+18=63\). Check: \(45\times 1.40=63\).
Answer: markup $18; selling price $63.
Problem 8: Markup on a bike
Markup: \(0.35\times 80=28\). Selling price: \(80+28=108\). Check: \(80\times 1.35=108\).
Answer: markup $28; selling price $108.
Problem 9: Percent off
Discount in dollars: \(90-63=27\). Divide by the regular price: \(\frac{27}{90}=0.30=30\%\).
Check: \(0.30\times 90=27\) and \(90-27=63\). Answer: 30% off.
Problem 10: Commission
- \(0.05\times 3200=160\).
- \(0.05\times S=200\), so \(S=200: 0.05=4000\). Check: \(0.05\times 4000=200\).
Answer: (a) $160; (b) $4,000 in sales.
Problem 11: Pay with commission
Commission: \(0.03\times 8{,}500=255\). Total pay: \(400+255=655\).
Answer: commission $255; total pay $655.
Problem 12: Simple interest
\(I=Prt=1200\times 0.025\times 3\). First, \(1200\times 0.025=30\) dollars per year. Then \(30\times 3=90\). Balance: \(1200+90=1290\).
Answer: interest $90; balance $1,290.
Problem 13: Time to earn interest
- \(I=Prt=1{,}500\times 0.03\times 1=45\) dollars per year.
- The interest grows by $45 each year, so \(45t=180\) and \(t=180: 45=4\). Check: \(1{,}500\times 0.03\times 4=180\).
Answer: (a) $45; (b) 4 years.
Problem 14: Finding the original price
The sale price is \(100\%-30\%=70\%\) of the original. So \(0.70\times P=21\) and \(P=21: 0.70=30\). Check: \(30\times 0.70=21\).
Answer: $30.
Problem 15: Price before tax
The total is \(100\%+7\%=107\%\) of the price before tax, so \(1.07\times P=53.50\).
\(P=53.50: 1.07=50\). Tax: \(53.50-50=3.50\).
Check: \(0.07\times 50=3.50\) and \(50+3.50=53.50\). Answer: $50.00 before tax; tax $3.50.
Problem 16: Discount then tax
Sale price: \(85\times 0.80=68\). Tax: \(68\times 0.08=5.44\). Total: \(68+5.44=73.44\).
Answer: $73.44.
Problem 17: Sale plus coupon
- \(0.80\times 50=40\), so the sale price is $40.
- \(0.90\times 40=36\), so the final price is $36.
- Savings: \(50-36=14\). \(\frac{14}{50}=0.28=28\%\).
Answer: (a) $40 (b) $36 (c) 28% savings.
Problem 18: Ticket fees
Tickets: \(4\times 45=180\). Service fee: \(0.12\times 180=21.6\). Total: \(180+21.6+5=206.6\).
Answer: $206.60.
Problem 19: Group dinner bill
- Tax: \(0.08\times 64=5.12\). Tip: \(0.20\times 64=12.80\).
- Total: \(64+5.12+12.80=81.92\).
- Each friend: \(81.92: 4=20.48\).
Answer: (a) tax $5.12, tip $12.80 (b) $81.92 (c) $20.48 each.
Problem 20: Comparing savings plans
- Plan A: \(2000\times 0.03\times 5=300\). Plan B: \(1800\times 0.04\times 5=360\).
- Plan A: \(2000+300=2300\). Plan B: \(1800+360=2160\).
- Plan B earns $60 more interest, but Plan A ends with \(2300-2160=140\) dollars more because it starts with more money.
Answer: (a) $300 and $360; (b) $2,300 and $2,160; (c) Plan B earns more interest, Plan A ends with more money.
See every chapter on the Grade 7 math page.