Question

A sports store I'd having a sale on soccer balls. A soccer coach purchases 10 soccer balls and 2 soccers bags for $155. Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189. What is the cost of a soccer ball and the cost of a soccer ball ?

Answer 1

- The price of a soccer ball is $14.5

- The price of a soccer bag is $5

Explanation:

To solve this problem, we call:

s = the price of a single soccer ball

b = the price of a soccer bag

We have:

1) A soccer coach purchases 10 soccer balls and 2 soccers bags for $155: so we can write

`10s+2b=155` (1)

2) Another scorer coach purchases 12 soccer balls and 3 soccer bags for $189: so we can write

`12s+3b=189` (2)

So we have a system of two equations in two unknown variables:

`10s+2b=155\\12s+3b=189`

We solve it by multiplying eq.(1) by 3 and eq(2) by 2, and we get:

`30s+6b=465\\24s+6b=378`

Now we substract eq(2) from eq(1) and we get:

`6s=87`

So

`s=(87)/(6)=14.5`

And by using eq(1) we also find the value of b:

`10s+2b=155\\b=(155-10s)/(2)=(155-10(14.5))/(2)=5`

So:

- The price of a soccer ball is $14.5

- The price of a soccer bag is $5