Question

You spend $132 on clothes. Shirts cost $12 and pants cost $16. You buy a total of 9 items. A. Write a system of linear equations that represents this situation. B. Solve the system and interpret your solution.

Answer 1

Answer:

a.

x+y=9 (1)

12x+16y=132 (2), where:

x is the number shirts

y is the number of pants

b. You bought 3 shirts and 6 pants.

Explanation:

The first equation would indicate that the number of shirts plus the number of pants is equal to 9:

x+y=9

The second equation would indicate that the price per shirt for the number of shirts plus the price per pant plus the number of pants is equal to 132:

12x+16y=132

The system of of linear equations that represents this situation is:

x+y=9 (1)

12x+16y=132 (2), where:

x is the number shirts

y is the number of pants

You can solve for x in (1):

x=9-y (3)

Then, you can replace (3) in (2):

12(9-y)+16y=132

108-12y+16y=132

4y=24

y=24/4

y=6

Now, you can replace the value of y in (3):

x=9-6

x=3