Two brothers went shopping at a back to school sale where all shirts and shorts are the same price. The younger brother spent $175 on 7 new shirts and 7 pairs of shorts. The older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $165. Write the system of equations for this problem.

Each shirt costs $ 10, while each short costs $ 15.

Step-by-step explanation:

Since two brothers went shopping at a back to school sale where all shirts and shorts are the same price, and the younger brother spent $ 175 on 7 new shirts and 7 pairs of shorts while the older brother purchased 6 new shirts and 7 pairs of shorts and paid a total of $ 165, to determine the price of each shorts and each shirt the following system of equations must be considered:

Shirt = X

Short = Y

7X + 7Y = 175

6X + 7Y = 165

7X - 6X + 7Y - 7Y = 175-165

X = 10

7x10 + 7Y = 175

70 + 7Y = 175

7Y = 175 - 70

Y = 105/7

Y = 15

Thus, each shirt costs $ 10, while each short costs $ 15.

3x + 4y =108

7x + 5y =114