Question

The marching band sells cases of oranges and grapefruit for a fundraiser. Shakira sells 5 cases of oranges and 8 cases of grapefruit for $235. Jeff sells 3 cases of oranges and 2 cases of grapefruit for $85. How much would 1 case of each fruit cost altogether?

Answer 1

Cost of 1 case of oranges is $ 15 and cost of 1 case of grapefruits is $ 20

(Cost of 1 case of oranges and 1 case of grapefruits altogether equal to
`15+20=\$35`)

Explanation:

Let cost of 1 case of oranges be
`\$x` and cost of 1 case of grapefruits be
`\$y`

As cost of 5 cases of oranges and 8 cases of grapefruit is $235,

`5x+8y=235` ...(i)

As cost of 3 cases of oranges and 2 cases of grapefruit is $85,

`3x+2y=85` ...(ii)

Multiply equation (ii) by
`-4`

`-12x-8y=-340` ...(iii)

Add (i) and (iii)

`-7x=235-340\\-7x=-105\\x=(-105)/(-7)\\ =15`

Put
`x=15` in (i)

`5(15)+8y=235\\75+8y=235\\8y=235-75\\8y=160\\y=(160)/(8)=20`

So,

Cost of 1 case of oranges is $ 15 and cost of 1 case of grapefruits is $ 20

Therefore,

Cost of 1 case of oranges and 1 case of grapefruits altogether equal to
`15+20=\$35`