Use a system of equations to solve the following problems. See the earlier examples.

An investor decides at the beginning of the year to invest some of his cash in an account paying $8 \%$ annual interest, and to put the rest in a stock fund that ends up earning $15 \%$ over the course of the year. He puts $\$ 2000$ more in the first account than in the stock fund, and at the end of the year he finds he has earned $\$ 1310$ in interest. How much money was invested at each of the two rates?

Sharon Donald has a credit card with an APR on purchases of $16 \%$. The balance transfer APR is ${8 \%}$ and there is a $2 \%$ balance transfer fee.

How much will she pay in fees to transfer $\$ 500$ to the card?

Analyzing a Spending Plan. Carl's house payment is $\$ 1,050$ per month and his car payment is $\$ 385$ per month. If Carl's take-home pay is $\$ 2,800$ per month, what percentage does Carl spend on his home and car?

How does Poe use personification in "The Fall of the House of Usher"?

Use a system of equations to solve the following problems. See the earlier examples.

Eliza's mother is 20 years older than Eliza, but 3 years younger than Eliza's father. Eliza's father is 7 years younger than three times Eliza's age. How old is Eliza?

The annual percentage rate (APR) is always a. greater than the APY. b. less than or equal to the APY. c. the same as the APY.

Use a system of equations to solve the following problems. See the earlier examples.

What choice of a, b, and c will force the graph of the polynomial $f(x)=a x^2+b x+c$ to have a $y$-intercept of 5 and to pass through the points $(1,3)$ and $(2,0)$?

Use a system of equations to solve the following problems. See the earlier examples.

Karen empties out her purse and finds 45 loose coins, consisting entirely of nickels and pennies. If the total value of the coins is $\$ 1.37$, how many nickels and how many pennies does she have?

The following data apply to Pro Beauty Supply Inc. for May 2016:

1. Balance per the bank on May 31, $9,150.

2. Deposits in transit not recorded by the bank,$1,510.

3. Bank error; check written by Best Beauty Supply was charged to Pro Beauty Supply's account, $560.

4. The following checks written and recorded by Pro Beauty Supply were not included in the bank statement:

$$\begin{array}{lrr} \text{3013}&&\$ \hspace{9pt}510\\ \text{3054}&&\text{640}\\ \text{3056}&&\text{1,520}\\ \end{array}$$

5. Note collected by the bank, $500.

6. Service charge for collection of note,$20.

7. The bookkeeper recorded a check written for $320 to pay for the May utilities expense as$230 in the cash disbursements journal.

8. Bank service charge in addition to the note collection fee, $40.

9. Customer checks returned by the bank as NSF,$310.

Required

Determine the amount of the unadjusted cash balance per Pro Beauty Supply's books.

Evaluate the following determinant. See the earlier example.

$$\left|\begin{array}{ll}w & x \\ y & z\end{array}\right|$$

Suppose your salary in 2015 is $40,000. Assuming an annual inflation rate of 7%, what salary do you need to earn in 2020 in order to have the same purchasing power?

Suppose that money is deposited steadily in a savings account so that $14,000 is deposited each year. Determine the balance at the end of 6 years if the account pays 4.5% interest compounded continuously.

Determine the simple interest owed on $860 for 3 years at a rate of 12.5%.

Fill in the blanks in the following statements.

A store is having a $40 \%$ off sale. The sale price for an item with a regular cost of $\$ 80$ is $\underline{\qquad \qquad}$.