Question

Paul and Darry are selling fruit for a school fundraiser. Customers can buy small boxes of grapefruit. Paul sold 5 boxes of grapefruit and 8 boxes of grapefruit for a total of $115. Darry sold 6 small boxes of grapefruit and 5 large boxes of grapefruit for a total of $92. what is the cost of each of one small box of grapefruit and 5 large box of grapefruit?

solve by using elimination or substitution show all work . cpa2 math

heres the 2 equations i got 5x+8y=115 and 6X+5y=92

please help I have been stuck on this 4 days

Answer 1

57

Explanation:

5x+8y=115

6x+5y=92

We can either use substitution or elimination. I prefer elimination

Multiply the first equation by 6 and the second equation by -5 to eliminate x

6(5x+8y)=115*6

30x +48y = 690

The second equation

-5( 6x+5y)=92*-5

-30x -25y =-460

Add the two equations together

30x +48y = 690

-30x -25y =-460

-------------------------

23y = 230

Divide each side by 23

23y/23 = 230/23

y = 10

Now we need to find x

6x+5y=92

6x+5(10) = 92

6x+50 =92

Subtract 50 from each side

6x +50-50 = 92-50

6x = 42

Divide by 6

6x/6 = 42/6

x = 7

We want to find the cost of 1 small grapefruit and 5 large grapefruit

x +5y

7 + 5(10)

7+50

57

Answer 2

Explanation:

Alright, lets gets started.

If x is the price of small box and y is the price of large box.

You have made both equations, absolutely correct.

`5x+8y=115` .................. equation (1)

`6x+5y=92` .................... equation (2)

Multiplying by 5 in equation (1) and multiplying by 8 in equation (2)

`25x+40y=575` .................. equation (3)

`48x+40y=736` ................... equation (4)

Subtracting equation 4 and equation (3)

`48x-25x=736-575`

`23x=161`

`x=7`

Plugging the value of x in equation (1)

`5*7+8y=115`

`35+8y=115`

`8y=115-35`

`8y=80`

`y=10`

So, cost of 5 large box of fruit =
`5y = 5*10=50`

one small box of grapefruit and 5 large box of grapefruit will be =
`7+50=57`

So, cost of each of one small box of grapefruit and 5 large box of grapefruit is $ 57. : Answer

Hope it will help :)