Question

2. Mac is buying some new clothes for work. At the first store, he bought 3 shirts and 2 pants for $45. At

the second store he bought 2 shirts and 5 pants for $74. How much did each item cost?
Define your variables. x =
Write a system of equations..
Solve using any method. Then answer the questions with correct units.
y=_

Answer 1

Let x be the cost of each shirt and y be the cost of each pant.

From the first store, we know that 3x + 2y = 45
From the second store, we know that 2x + 5y = 74

We can use substitution or elimination method to solve for x and y.

By substitution, solving for x in the first equation:

3x + 2y = 45
3x = 45 - 2y
x = 15 - 2/3 y

Substituting this into the second equation:

2 (15 - 2/3 y) + 5y = 74
30 - 4/3 y + 5y = 74
30 + 1/3 y = 74
1/3 y = 44
y = 132

Now that we have found the value of y, we can substitute it back into x = 15 - 2/3 y to find x:

x = 15 - 2/3 * 132 = 15 - 88/3 = 15 - 29.33 = $-14.33

However, the cost of each item cannot be negative, so this solution does not make sense. This indicates that there is no solution to this system of equations and Mac cannot have bought these items for the given prices.