Rational Equations in Financial Contexts — Quiz Answers

A family spends $⁢2,984 per month on necessities. They decide to save 12% of their gross income for a vacation. They want the ratio of necessities and vacation savings to gross income to equal 0.65 Complete the equation they can use to find the monthly gross income, x , they need to earn to meet these goals.

A couple spends $⁢3,200 on necessities each month. They would like to save 6% of their gross income for a vacation. They want the ratio of necessities and vacation savings to gross income to equal 0.6 Which equation can they use to find the monthly gross income, x , they need to earn to meet these goals?

An investor has $⁢25,000 to invest in stocks and bonds. She wants the ratio of stocks to bonds to be 3 to 2 Which equation can she use to find the amount to invest in bonds, x ?

An investor is buying more shares of a stock that is currently trading at $⁢24.89 Previously, he bought 250 shares of this stock for $⁢6,304 He wants the average purchase price of all the shares to be $⁢19.55 The average purchase price is the total amount spent divided by the total number of shares. Complete the equation that he can use to find how many shares to buy to achieve his desired average purchase price.

A start-up wants to make a product at an average cost of $⁢2.75 apiece. You can find the average cost of production by dividing the cost to produce a certain number of units, x , by the number of units. The cost of production includes a setup fee of $⁢1,200 and a cost per unit of $⁢1.85 Which equation can find the number of units that fit into the start-up's budget?

A person has $⁢15,000 to invest in stocks and bonds. They would like the ratio of stocks to bonds to be 4 to 5 Complete the equation they can use to find the amount in stocks, x

An investor purchased 300 shares of a stock for $⁢2,604 He is buying more shares at a rate of $⁢12.20 He wants the average purchase price of all the shares to be $⁢10.15 The average purchase price is the total amount spent divided by the total number of shares. Which equation can he use to find the number of shares to buy to achieve his desired average purchase price?

An employee wants to save 18% of her gross income for retirement. Her company contributes 4.5% of each employee's gross income to a retirement savings account. The employee is also saving $⁢75 per paycheck. Complete the equation to determine what the employee's gross income, x , needs to be for the savings rate to be 18%

A company has determined that a new product needs to have an average cost of production of $⁢12.75 per unit. To find the average cost of production, divide the cost to produce a certain number of units, x , by the number of units. The supplier has a setup fee of $⁢3,600 and a cost per unit of $⁢9.84 Complete the equation that can be used to find the number of units the company should order to achieve this average cost of production.

An employee saves $⁢55 per paycheck in addition to 4.25% of his gross income. An advisor says his savings-to-income ratio should be 1 to 5 Complete the equation the employee can use to determine the amount he must make, x , with this savings structure to follow the advisor's recommendation.

The total cost to produce an item includes a setup fee of $⁢2,200 and $⁢12.25 per unit. A customer wants to keep the average production cost at $⁢15.00 per unit. The average production cost is the cost to produce a certain number of units, x , divided by the number of units. How many units, x , should the customer order to achieve this average cost per unit? Round to the nearest unit if necessary.

An investor has $⁢150,000 in an investment account and is making a deposit. They would like the ratio of the deposit, x , to the total investment to be (1)/(10) Complete the equation the investor can use to find the amount they need to deposit to meet their goal.

An investor has $⁢108,000 in an investment account and is going to make an additional deposit. She would like the ratio of the deposit, x , to the total investment to be (1)/(12) Which equation can she use to find the amount she needs to deposit to meet her goal?

An employee wants to save 12% of his gross income for retirement. His company contributes 4.8% of each employee's gross income to a retirement savings account. He is also saving $⁢210 per month. Given the current savings plan, what gross monthly income, x , must the employee earn to have a 12% rate of retirement savings? Round to the nearest dollar if necessary.

An investor has $⁢55,000 in an investment account and is making a deposit. He would like the ratio of the deposit, x , to the total account value after the deposit to be (1)/(11) How much should he deposit to meet his goal? Round to the nearest whole number if necessary.

An investor has $⁢45,000 in an investment account and is making an additional deposit. He would like the ratio of the deposit, x , to the total account value after the deposit to be (1)/(10) How much should he deposit to meet this goal? Round to the nearest whole number if necessary.

An investor purchased 1,000 shares of a stock for $⁢52,350 She is buying more shares at the current rate of $⁢91.27 She wants the average purchase price of all the shares to be $⁢85 The average purchase price is the total amount spent divided by the total number of shares. How many shares should she buy to achieve her desired average purchase price? Round to the nearest whole number if necessary.

Investors in a start-up will split $⁢15,000 in dividends evenly between them. If 25 more investors are added, the dividends will decrease by $⁢20.00 Use the equation and a graphing calculator to determine how many investors the original business plan includes. the fraction with numerator 15 comma 000 and denominator x minus 20 is equal to the fraction with numerator 15 comma 000 and denominator x plus 25

An investor has $⁢16,000 to invest in stocks and bonds. An advisor recommends a ratio of (3)/(5) stocks to bonds. How much should the investor put into stocks, x , to achieve this ratio?

An investor purchased 250 shares of a stock for $⁢50,500 She is buying more shares at the current rate of $⁢267.14 She wants the average purchase price of all the shares to be $⁢240 The average purchase price is the total amount spent divided by the total number of shares. How many shares should she buy to achieve her desired average purchase price? Round to the nearest whole number if necessary.