Question

8 friends started a business. They will wear either a baseball cap or a shirt imprinted with their logo while working. They want to spend exactly $36 on the shirts and caps. Shirts cost $6 each and caps cost $3 each. Write a system of equations to describe the situation. Let x represent the number of shirts and y represent the number of caps.

Graph the system. What is the solution and what does it represent?

Answer 1

We can write this system of equations:

6x + 3y = 36
x + y = 8

If you graph this, it gives you a solution of (4, 4)

This tells us that the friends must buy 4 shirts and 4 caps in order to spend exactly $36 and to have 8 items total.

Answer 2

For this case, the first thing we must do is define variables.

We have then:

y: number of caps

x: number of shirts

We now write the system of equations that represents the problem:

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The graphical solution of the system of equations (see attached image) is:

`image`

Therefore, we have 4 shirts and 4 caps.

Answer:

`image`

See attached image for the graphic

number of caps = 4

number of shirts = 4