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

8 friends

so s=number of shirts
c=number of caps

c+s=8
6 per shirt and 3 per cap therefor the price totalis
36=caps+shirts
36=3c+6s
so we have the equations

c+s=8
3c+6s=36

simplify second equaiton by divide by 3
c+2s=12
c+s=8
we can see that froma difference of 1s, the result changes +4 so therefor s=4
subsitute
c+4=8
4+4=8
c=4


sorry, can't graph easily on this site

the solution is 2 lines, that intersect at one point which is (4,4) which represents 4 shirts and 4 caps

Answer 2

We know that there are 8 shirts and caps in total (because there are 8 friends). Therefore, we have the first equation:
x+ y= 8

All shirts cost: 6x (dollars) (because each shirt costs 6 dollars)
All caps cost: 3y (dollars) (because each cap costs 3 dollars)
The total price is 36 dollars, so we have another equation:
6x+ 3y= 36

x+y= 8 (1)
6x+ 3y= 36 (2)

Multiply (1) by 3, we have:
3x+ 3y= 24 (3)

Take (2) minus (3), we have:
(6x -3x)+ (3y -3y)= 36-24
⇒ 3x= 12
⇒ x= 12/3
⇒ x= 4

x+y= 8
⇒ y= 8-x= 8-4= 4

Final answer: x=4, y=4~
They will buy 4 shirts and 4 caps~