Question

q. on the first day of a sale at runway clothing, all jeans were $25 and all shirts were $22. the store took in $686.

on the second day, the store reduced the price of both jeans and shirts to $20 each. it sold exactly the same number of each item as it had on the first day.

if the store made $580 on the second day, how many shirts did they sell in all during the two-day sale?

a. 13
b. 16
c. 26
d. 32

Explanation:

Define variables and set up the first equation

Using the Systems of Equations knowledge point
Let \(j\) be the number of jeans sold on the first day, and \(s\) be the number of shirts sold on the first day.
On Day 1, jeans cost \$25 and shirts cost \$22, with total revenue of \$686:

$$25j + 22s = 686$$

Set up the second equation

Using the Systems of Equations knowledge point
On Day 2, the store sold the same quantities \(j\) and \(s\) at \$20 each, making \$580:

$$20j + 20s = 580$$

Simplify the second equation

Using the Systems of Equations knowledge point
Divide the second equation by 20:

$$j + s = 29$$

Solve the system of equations

Using the Elimination Method and Substitution Method knowledge points
Express \(j\) in terms of \(s\):

$$j = 29 - s$$

Substitute into the first equation:

$$25(29 - s) + 22s = 686$$

$$725 - 25s + 22s = 686$$

$$725 - 3s = 686$$

$$3s = 39 \implies s = 13$$

Calculate the total shirts sold

Using the Systems of Equations knowledge point
The store sold \(s = 13\) shirts on Day 1 and the same number on Day 2.
Total shirts sold over both days:

$$13 + 13 = 26$$

Answer:

• (A) 13
• (B) 16
• (C) 26 (Correct answer)
• (D) 32