Question

1. a business borrows $1,500 at an interest rate of 6.95%. what is the total that the business will owe after 7 years?
2. a person buys a meal.

• a 9% sales tax was applied to the original cost.
• she tips 19% on the original cost.
• she pays a total of $23.35.

what was the original cost of her meal?

1. a golfer wants to buy a new set of golf clubs. the same set is sold at two different stores.

• store #1 has a 20%-off sale. its sale price will be $120.
• store #2 sells the golf clubs for $8.00 less than store #1’s original price.
• store #2 is having a 13% off sale.

what is the total cost of the golf clubs at the second store?

1. a student compares his height at the beginning and end of middle school.

• he was 54 inches tall at the beginning.
• he was 172 cm tall at the end.

1 in ≈ 2.54 cm
what is the percent change of the student’s height from the beginning of middle school to the end of middle school? round to the nearest whole number percent.

1. a family invests $5225 in an account that earns simple interest each year. after 42 months, the account’s value is $5868.25.

12 months = 1 year
what is the simple interest rate? round to the nearest tenth.

Explanation:

Problem 13

Step1: Define the original cost

Let the original cost of the meal be \( x \) dollars. The sales tax is \( 9\% \) of \( x \), which is \( 0.09x \), and the tip is \( 19\% \) of \( x \), which is \( 0.19x \). The total amount paid is the sum of the original cost, tax, and tip, so the equation is \( x + 0.09x + 0.19x = 23.35 \).

Step2: Combine like terms

Combine the terms on the left side: \( x(1 + 0.09 + 0.19) = 23.35 \), so \( 1.28x = 23.35 \).

Step3: Solve for \( x \)

Divide both sides by \( 1.28 \): \( x=\frac{23.35}{1.28} \approx 18.24 \).

Step1: Find Store #1's original price

Let the original price at Store #1 be \( p \). A \( 20\% \)-off sale means the sale price is \( 80\% \) of \( p \), so \( 0.8p = 120 \). Solve for \( p \): \( p=\frac{120}{0.8}=150 \) dollars.

Step2: Find Store #2's original price

Store #2's original price is \( 150 - 8 = 142 \) dollars (since it's \(\$8\) less than Store #1's original price).

Step3: Apply Store #2's discount

Store #2 has a \( 13\% \)-off sale, so the sale price is \( 87\% \) of \( 142 \). Calculate \( 0.87\times142 \): \( 0.87\times142 = 123.54 \) dollars.

Step1: Convert initial height to cm

The initial height is \( 54 \) inches. Using \( 1 \) in \( \approx 2.54 \) cm, the initial height in cm is \( 54\times2.54 = 137.16 \) cm.

Step2: Calculate the change in height

The final height is \( 172 \) cm, so the change in height is \( 172 - 137.16 = 34.84 \) cm.

Step3: Calculate the percent change

The percent change formula is \( \frac{\text{Change}}{\text{Original}} \times 100\% \). So, \( \frac{34.84}{137.16} \times 100\% \approx 25.4\% \), which rounds to \( 25\% \).

Answer:

The original cost of her meal is approximately \(\$18.24\).

Problem 14