Percent Word Problems - Accuplacer Arithmetic

1. In a city, 60% of the population are registered voters. Of the registered voters, only 45% actually voted in the last election. What percentage of the total city population voted in the last election?
   Answer: 27% To find the percentage of the total population that voted, you must find 45% of 60%. Convert the percentages to decimals and multiply: $0.45 \times 0.60 = 0.27$. Converting this decimal back to a percentage gives 27%.
2. A real estate agent earns a 3% commission on the selling price of a house. If the agent earned a commission of $8,850, what was the selling price of the house?
   Answer: $295,000 The commission is 3% of the selling price. Let S be the selling price. The equation is $0.03 \times S = \$8,850$. To find the selling price, divide the commission by the commission rate (as a decimal): $S = \$8,850 \div 0.03 = \$295,000$.
3. After a 15% discount, the price of a coat is $153. What was the original price of the coat?
   Answer: $180.00 The discounted price represents 100% - 15% = 85% of the original price. Let P be the original price. Then $0.85 \times P = \$153$. To find the original price, divide the discounted price by 0.85: $P = \$153 \div 0.85 = \$180.00$.
4. An electronics store sold a camera for $420, making a 20% profit on the cost. What was the store's cost for the camera?
   Answer: $350 The selling price ($420) is the store's cost (C) plus the profit (20% of C). So, $\$420 = C + 0.20C$, which simplifies to $\$420 = 1.20C$. To find the cost, divide the selling price by 1.20: $C = \$420 \div 1.20 = \$350$.
5. A bicycle is listed at $450. It is on sale for 20% off. If the sales tax is 6% on the sale price, what is the total cost of the bicycle?
   Answer: $381.60 First, calculate the discount amount: 20% of $450 is $0.20 \times 450 = \$90$. The sale price is the original price minus the discount: $\$450 - \$90 = \$360$. Next, calculate the sales tax on the sale price: 6% of $360 is $0.06 \times 360 = \$21.60$. The total cost is the sale price plus the tax: $\$360 + \$21.60 = \$381.60$.
6. A property tax assessment increases by $8\%$ this year. Additionally, the tax rate increases from $1.2\%$ to $1.35\%$ of assessed value. If a homeowner's tax bill was $2,400 last year, what will it be this year?
   Answer: $2,916 Last year's assessed value: $2,400 ÷ 0.012 = $200,000. This year's assessed value: $200,000 × 1.08 = $216,000. This year's tax: $216,000 × 0.0135 = $2,916. Choice B only applies the assessment increase. Choice C only applies the rate increase. Choice D incorrectly adds the percentage increases before calculating.
7. A retailer buys items for $40 each and wants to price them so that after offering a $20\%$ discount, the profit margin on the sale price will be $25\%$. What should be the original marked price?
   Answer: $66.67 Let x be the marked price. After 20% discount, sale price is 0.8x. For 25% profit margin on sale price: sale price = cost ÷ 0.75. So 0.8x = $40 ÷ 0.75 = $53.33. Therefore x = $53.33 ÷ 0.8 = $66.67. Choice A calculates margin on cost instead of sale price. Choice C uses wrong discount calculation. Choice D adds the percentages incorrectly.
8. A library has 1,500 books. 40% of the books are fiction. Of the non-fiction books, 25% are biographies. How many biographies does the library have?
   Answer: 225 First, find the number of fiction books: $0.40 \times 1,500 = 600$. The number of non-fiction books is the total minus the fiction books: $1,500 - 600 = 900$. Next, find the number of biographies by taking 25% of the non-fiction books: $0.25 \times 900 = 225$. The library has 225 biographies.
9. A principal amount of $2,500 is invested in an account with a simple annual interest rate of 4%. What is the total amount in the account after 3 years?
   Answer: $2,800.00 Simple interest is calculated using the formula I = Prt. The annual interest is $\$2,500 \times 0.04 = \$100$. Over 3 years, the total simple interest earned is $\$100 \times 3 = \$300$. The total amount in the account is the original principal plus the total interest: $\$2,500 + \$300 = \$2,800.00$.
10. A restaurant bill totals $84.60 before tax. The sales tax rate is $8.25\%$ and the customer wants to leave an $18\%$ tip on the pre-tax amount. What is the total amount the customer will pay?
    Answer: $106.81 Calculate tax: $84.60 × 0.0825 = $6.98. Calculate tip on pre-tax amount: $84.60 × 0.18 = $15.23. Total: $84.60 + $6.98 + $15.23 = $106.81. Choice A uses wrong tax rate. Choice C calculates tip on the after-tax amount. Choice D adds the percentages before multiplying.
11. A car depreciates $15\%$ in its first year and $12\%$ of its remaining value in its second year. If the car is worth $18,700 after two years, what was its original value?
    Answer: $25,000 After first year, the car is worth 85% of original value. After second year, it's worth 88% of the first year value, or 0.85 × 0.88 = 0.748 of original value. If 0.748 × original = $18,700, then original = $18,700 ÷ 0.748 = $25,000. Choice A uses simple depreciation instead of compound. Choice B miscalculates the decimal conversion. Choice D adds the depreciation percentages incorrectly.
12. A membership at a gym costs $50 per month. If a member pays for an entire year in advance, they receive a 15% discount on the total cost. How much does it cost to pay for a year in advance?
    Answer: $510.00 First, calculate the total cost for a year without a discount: $\$50 \times 12 = \$600$. Next, calculate the discount amount: 15% of $600 is $0.15 \times \$600 = \$90$. Finally, subtract the discount from the total yearly cost: $\$600 - \$90 = \$510$.
13. A rental car company charges a daily rate plus a 15% tax and fee surcharge. If the total charge for a one-day rental was $63.25, what was the company's daily rate before the surcharge?
    Answer: $55.00 The total charge of $63.25 represents 100% of the daily rate plus a 15% surcharge, which is 115% of the daily rate. Let R be the daily rate. Then $1.15 \times R = \$63.25$. To find the rate, divide the total charge by 1.15: $R = \$63.25 \div 1.15 = \$55.00$.
14. A savings account earned $67.50 in simple interest over one year at an annual interest rate of 3%. What was the principal amount in the account at the beginning of the year?
    Answer: $2,250.00 Simple interest (I) is calculated as Principal (P) times rate (r) times time (t). Here, I = $67.50, r = 0.03, and t = 1. The formula is $I = P \times r \times t$, so $\$67.50 = P \times 0.03 \times 1$. To find the principal, divide the interest by the rate: $P = \$67.50 \div 0.03 = \$2,250.00$.
15. A laptop computer is priced at $1,200. The store offers a 10% discount. However, the customer must also pay an 8% sales tax on the discounted price. What is the final amount the customer pays?
    Answer: $1,166.40 First, calculate the discount: $0.10 \times \$1,200 = \$120$. The discounted price is $\$1,200 - \$120 = \$1,080$. Next, calculate the sales tax on this discounted price: $0.08 \times \$1,080 = \$86.40$. The final amount is the discounted price plus the tax: $\$1,080 + \$86.40 = \$1,166.40$.
16. A customer paid a total of $53.50 for a sweater. This price included a 20% discount off the original price and then a 7% sales tax on the discounted price. What was the original price of the sweater?
    Answer: $62.50 Let P be the original price. The discounted price is $P \times (1 - 0.20) = 0.8P$. The final price after tax is $(0.8P) \times (1 + 0.07) = (0.8P) \times 1.07 = 0.856P$. We are given that the final price is $53.50. So, $0.856P = \$53.50$. To find P, divide by 0.856: $P = \$53.50 \div 0.856 = \$62.50$.
17. A restaurant bill, including a 5% tax and an 18% tip on the pre-tax amount, totaled $147.60. What was the amount of the bill before tax and tip were added?
    Answer: $120.00 Let B be the original bill amount. The tax is 0.05B and the tip is 0.18B. The total cost is $B + 0.05B + 0.18B = 1.23B$. We are given that the total is $147.60. So, $1.23B = \$147.60$. To find B, divide the total by 1.23: $B = \$147.60 \div 1.23 = \$120.00$.
18. A store marks up merchandise by $40\%$ above wholesale cost, then offers a $25\%$ discount during a sale. If an item's sale price is $63, what was the wholesale cost?
    Answer: $60.00 Work backwards from the sale price. If wholesale cost is x, then markup price is 1.4x, and sale price is 1.4x × 0.75 = 1.05x. Since 1.05x = $63, then x = $63 ÷ 1.05 = $60. Choice A applies the discount before the markup. Choice C assumes the $63 is before the discount. Choice D incorrectly adds the percentages.
19. A store offers two promotion options on a $100 appliance. Option A is a single 35% discount. Option B is a 25% discount, followed by an additional 10% discount on the reduced price. How much more money does a customer save by choosing the better option?
    Answer: $2.50 Option A savings: $0.35 \times \$100 = \$35.00$. For Option B, the first discount is $0.25 \times \$100 = \$25.00$, making the price $75.00. The second discount is $0.10 \times \$75.00 = \$7.50$. Total savings for Option B is $\$25.00 + \$7.50 = \$32.50$. Option A is the better option. The difference in savings is $\$35.00 - \$32.50 = \$2.50$.
20. A salesperson earns a monthly salary of $1,200 plus a 5% commission on all sales over $10,000. If the salesperson's total sales for the month were $35,000, what were their total earnings for the month?
    Answer: $2,450 First, determine the amount of sales eligible for commission: $\$35,000 - \$10,000 = \$25,000$. Next, calculate the commission earned on that amount: 5% of $25,000 is $0.05 \times \$25,000 = \$1,250$. Finally, add the base salary to the commission: $\$1,200 + \$1,250 = \$2,450$.

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