Question

Kiara spent $28 on 4 ribbons and 5 balloons. Sarah spent $28 on 8 ribbons and 3 balloons. All ribbons cost the same amount and all balloons cost the same amount. What is the cost of each ribbon and each balloon?

Answer 1

Given :

Kiara spent $28 on 4 ribbons and 5 balloons.

Sarah spent $28 on 8 ribbons and 3 balloons.

To Find :

The cost of each ribbon and each balloon.

Solution :

Let, cost of each ribbon is x and balloon is y.

For situation 1 :

4x + 5y = 28     ...1)

For situation 2 :

8x + 3y = 28    ...2)

Multiplying equation 1) by 2 and subtracting equation 2) by it :

2( 4x + 5y ) - ( 8x + 3y ) = 2 × 28 - 28

10y - 3y = 28

y = 4

Putting value of y in equation 1) , we get :

$x = \dfrac{28-(5\times 4)}{4}\\\\x = 2$

Therefore, the cost of each ribbon and each balloon is $2 and $4 respectively.