High School

1. Find 8.5% of $160.

2. If an attorney charges a fee of 35% on the amount of the settlement in a lawsuit, how much will the attorney earn from a $400,000 settlement?

3. If the sales price of a DVD is $20 and the markup on the cost is 34%, what is the cost?

4. An item is discounted (marked down) by 12.5% so that the sales price is $140. What was the original price?

5. An investment of $5,000 is made at a simple annual interest rate of 3%. How much additional money must be invested at a simple annual interest rate of 3.9% so that the total annual interest earned is 3.5% of the total investment?

6. Daniel invested a total of $40,000 in two funds, A and B. He earned 8% on his investment in fund A and 11% on his investment in fund B. If he earned a total of $3,650 for the year, how much did he invest in each fund?

7. Suppose you invest $2,000 in stock X with a 4% projected return and $6,000 in stock Y with a 5.75% projected return. What is the projected return from your investment in dollars? What is your projected return in percent?

8. An investment decreases in value by 30% in the first year and increases in value by 40% in the second year. What is the percent change in the investment after 2 years?

9. The overhead costs are 60% of labor costs, and the total of labor and overhead costs is $4,000. How much are labor and overhead costs, respectively?

10. If a soft drink distributor sells on average 30 cans of soda per hour, how many cases of soda on average will it sell per week? Assume the distributor is open 40 hours per week and a case contains 24 cans.

11. Suppose you own 30% of a company.
a. If you buy another 20% of the company, what percent will you own?
b. If you increase your share of the company by 20% of the portion that you already own, what percent of the company will you own?

12. Your return on investment A is 4.5% and your return on investment B is 3%. If the total of your investment is $75,000, how much should you invest in each fund to obtain a return of 4%?

13. Suppose you deposit a certain amount of money in one bank account that pays a simple annual interest of 1.2% and another amount of money in a second bank account that pays a simple annual interest of 0.8%. Express the total balance of the two accounts after 1 year in terms of two variables.

14. If the simple annual interest rate on a bond fund is 6.4%, what is the interest rate per quarter?

15. If the simple annual interest rate on a loan is 4.5%, what is the interest rate per month?

16. Suppose a store sells an average of 80 cases of soda per day. Assume that each case contains 24 cans of soda and that the store is open 10 hours per day. Find the average number of sodas that the store sells per hour.

17. An accounting firm completes 450 tax returns per week. The firm has 20 accountants and assumes a 5-day work week. On average, how many tax returns will an individual accountant complete per day?

18. A comedy club averages $105,000 in total expenses for their Saturday night venue, and averages $125,000 in revenue from admittance charges, food, and drink. Find the club’s average net profit margin.

19. A fitness center has a revenue of $50,000,000. To what amount do they need to hold down their COGS to achieve an 8% gross profit margin?

20. The CPI was 255.7 in 2019 and 258.8 in 2020. Use the CPI to find the rate of inflation from 2019 to 2020.

21. Suppose the indexed value of platinum was 100 on January 1, 2000, and 237.5 on January 1, 2020. If the price of an ounce of platinum was $410 on January 1, 2000, find the price of an ounce of platinum on January 1, 2020.

22. If the markup on the cost of a pair of jeans was 30%, find the gross profit margin.

23. If the gross profit margin was 12% on a smartphone, find the markup on the cost.

24. The CPI was 130.7 in 1990 and 195.3 in 2005. If the cost of household goods in 2005 was $5,400, use the CPI to find the cost of these same household goods in 1990.

25. What should a bookstore charge for a finance textbook if they want a 15% net profit margin and the average total expenses for each textbook is $120?

26. A certain company manufactures private jets at a cost of $5,000,000 each and sells them at a price of $6,500,000 each. The company also has annual fixed costs of $30,000,000.
a. What is their annual profit from the sale of 40 jets?
b. If x represents the number of jets sold in a year, find the equation for the profit in one year.
c. How many jets does the company have to sell in order to make a profit of $15,000,000?
d. How many jets does the company have to sell in order to break even?
e. How many jets does the company have to sell in order to have a 9.4% profit margin?

Answer :

1. $13.60. 2. $140,000. 3. $14.93. 4. $160.

5. Invest an additional approximately $4,428.57 at 3.9%. 6. Daniel invested approximately $15,625 in fund A and approximately $24,375 in fund B. 7. The projected return in stock X is $80, and in stock Y, it's $345. 5.31%.

8. The percent change is an increase of 4%. 9. Labor costs are $2,000, and overhead costs are $1,200. 10. The distributor will sell approximately 50 cases. 11a. You will own 50% b. You will own 36%

12. You should invest $30,000 in investment A and $45,000 in investment B. 13. The total balance of the two accounts after 1 year can be expressed as 1.012x + 1.008y. 14. The interest rate per quarter is 1.6%. 15. The interest rate per month is 0.375%.

How did we get the values?

1.) To find 8.5% of $160, multiply 0.085 by $160. This equals $13.60.

2.) If an attorney charges a fee of 35% on a $400,000 settlement, the attorney will earn $140,000 from the settlement.

3.) To find the cost of a DVD with a $20 sales price and a 34% markup, divide $20 by 1 + 0.34. The cost is approximately $14.93.

4.) If an item is discounted by 12.5% and the sales price is $140, you can find the original price by dividing $140 by 0.875. The original price was $160.

5.) To achieve a total annual interest of 3.5% on a $5,000 investment at 3% interest, you need to invest an additional amount at 3.9%. Let x be the additional amount. Solve the equation: 0.03 * 5000 + 0.039 * x = 0.035 * (5000 + x) to find x, which is approximately $4,428.57.

6.) Let A be the amount invested in fund A and B be the amount invested in fund B. You can set up the following system of equations:

- A + B = $40,000 (total investment)

- 0.08A + 0.11B = $3,650 (total earnings)

Solve this system to find A and B. A is approximately $15,625, and B is approximately $24,375.

7.) The projected return from stock X is 4% of $2,000, which is $80. The projected return from stock Y is 5.75% of $6,000, which is $345. The total projected return is $80 + $345 = $425. The projected return in percent is (425 / 8000) * 100% ≈ 5.31%.

8.) To calculate the percent change in an investment that decreases by 30% and then increases by 40%, use the formula: ((1 - 0.30) * (1 + 0.40) - 1) * 100%. The percent change after 2 years is an increase of 4%.

9.) Let L be labor costs and O be overhead costs. You have two equations:

- O = 0.60L (overhead costs are 60% of labor costs)

- L + O = $4,000 (total labor and overhead costs)

Substitute the first equation into the second equation to solve for L and O. L is $2,000, and O is $1,200.

10.) If the distributor sells 30 cans per hour and is open 40 hours per week, they sell a total of 30 * 40 = 1200 cans per week. Since a case contains 24 cans, they will sell 1200 / 24 = 50 cases per week on average.

11.) a) If you own 30% of a company and buy another 20%, you will own a total of 30% + 20% = 50% of the company.

b) If you increase your share of the company by 20% of the portion that you already own, you will own 30% + (20% * 30%) = 30% + 6% = 36% of the company.

12.) Let's call the amount you should invest in investment A as "x" and in investment B as "y." We have two equations:

- x + y = $75,000 (total investment)

- 0.045x + 0.03y = 0.04 * $75,000 (desired total return)

Solve this system to find the values of x and y. You'll find that x is $30,000, and y is $45,000.

13.) Let's call the amount deposited in the first account "x" and in the second account "y." After 1 year, the total balance in the first account is x + 0.012x = 1.012x, and in the second account, it's y + 0.008y = 1.008y. So, the total balance is expressed as 1.012x + 1.008y.

14.) To find the interest rate per quarter when the simple annual interest rate is 6.4%, divide 6.4% by 4 (since there are four quarters in a year). The interest rate per quarter is 1.6%.

15.) To find the interest rate per month when the simple annual interest rate is 4.5%, divide 4.5% by 12 (since there are 12 months in a year). The interest rate per month is 0.375%.

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