Question

1. a business borrows $1,500 at an interest rate of 6.5%. 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. his sale price will be $120.
• store #2 sells the golf clubs for $81.00 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 original cost

Let the original cost of the meal be \( x \).

Step2: Calculate total cost formula

The sales tax is \( 9\% \) of \( x \), so tax is \( 0.09x \). The tip is \( 19\% \) of \( x \), so tip is \( 0.19x \). Total cost is original cost + tax + tip, so \( x + 0.09x + 0.19x = 23.35 \).

Step3: Simplify and solve

Combine like terms: \( 1.28x = 23.35 \). Then \( x=\frac{23.35}{1.28} \approx 18.24 \).

Step1: Find original price of Store #1

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

Step2: Find Store #2's original price

Store #2's original price is \( 150 - 8 = 142 \).

Step3: Calculate Store #2's sale price

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

Step1: Convert initial height to cm

Initial height is 54 inches. Since \( 1 \text{ in} = 2.54 \text{ cm} \), initial height in cm is \( 54\times2.54 = 137.16 \) cm.

Step2: Calculate percent change

Percent change formula is \(\frac{\text{New - Old}}{\text{Old}}\times100\). New height is 172 cm, old is 137.16 cm. \(\frac{172 - 137.16}{137.16}\times100=\frac{34.84}{137.16}\times100\approx25.4\%\), rounded to nearest whole number is \(25\%\).

Answer:

The original cost of the meal is approximately \(\$18.24\) (if we need to round to two decimal places, or adjust as per context).

Problem 14