Question

Steve is making punch for a party. The recipe requires twice as much orange juice as cranberry juice and 8 times as much ginger ale as cranberry juice. If he plans to make 176 ounces of punch, how much each ingredient should he use ?

Answer 1

Let the amount of orange juice is represented by x ounces, cranberry juice is represented by y ounces and ginger ale is represented by z ounces.

Since, the orange juice is twice the cranberry juice, we get

`x=2y` ..... (1)

ginger ale is 8 times the cranberry juice.

`z=8y` ... (2)

The total amount is given is 176 ounces

=>
`x+y+z= 176` .... (3)

Substituting the values of x and z in terms of y in equation 3.

`2y+8y+y=176 11y = 176 y = 16 ounce`

Hence Orange juice = 2*16 = 32 ounce

Ginger Ale = 8*16 = 128 ounce

Cranberry juice = 16 ounce

Answer 2

Let the amount of cranberry juice used for making fruit punch = x

Since, the recipe requires twice as much orange juice as cranberry juice.

So, the amount of orange juice used for making fruit punch =
`2 * x = 2x`

Since, the recipe requires 8 times as much ginger ale as cranberry juice.

So, the amount of ginger ale used for making fruit punch =
`8 * x = 8x`

Since, he plans to make 176 ounces of punch.

So, x+2x +8x = 176

11x = 176

x =
`(176)/(11)`

x = 16.

Amount of cranberry juice = 16

Amount of orange juice = 2x = 2 x 16 = 32

Amount of ginger ale = 8x = 8 x 16 = 128