Question

Last week, Shane bought 14 shirts and 8 hats for a total of $146. Today, Shane bought 26 shirts and 9 hats for a total of $236. Assuming neither item has changed in price, what is the cost of a shirt in dollars?

A) $6

B) $7

C) $8

D) $9

Answer 1

The problem was solved by setting up a system of equations from the two scenarios provided, then solving algebraically to find that the cost of a shirt is $7.

Step-by-step explanation:

The student's question asks us to determine the cost of a shirt given two separate shirt and hat purchase scenarios with their corresponding total costs. To solve this problem, we create a system of equations based on the given scenarios and use algebraic methods to solve for the price of one shirt.

Solving the System of Equations

Let s be the cost of a shirt and h be the cost of a hat. From the first scenario (14 shirts and 8 hats for $146), we get the equation:

14s + 8h = 146 (1)

From the second scenario (26 shirts and 9 hats for $236), we get another equation:

26s + 9h = 236 (2)

To find the value of s, we can multiply equation (1) by 9 and equation (2) by 8 and then subtract the two results to eliminate h.

9(14s + 8h) = 9(146)

8(26s + 9h) = 8(236)

By subtracting the two new equations:

• 126s + 72h = 1314
• 208s + 72h = 1888

We get:

• 82s = 574

Dividing both sides by 82 gives us s = $7.

The cost of a shirt in dollars is $7.