Question

A store manager is ordering shirts for $5 each and pants for $8 each. She buys a total of 80 items at a cost of $430. The system of equations {x+y=805x+8y=430 can be used to solve for the number of shirts, x, and the number of pairs of pants, y, the manager orders.

What is the solution?

Answer 1

Given the equaiton system, we can use the method of solving two equations to find the answer:

x+y=80

5x+8y=430

Break it down into two equaitons:

x+y = 80

y = 80 - x ...(1)

5x + 8y = 430...(2)

We can then use the method of substitution to find the answers:

Put (1) into (2),

5x + 8(80-x) = 430
5x + 640 - 8x = 430
-3x = 430 - 640
-3x = -210
x = 210/3
x = 70...(3)

Now thay we find x, we can put it into the first eqaution to find y:

x+y = 80
70+y = 80
y = 10

Therefore, x= 70 and y = 10.

Hope it helps!