Question

A brand of grape juice that's is 25% grape juice is mixed with another brand that is 75% grape juice. The result is 7 gallons of grape drink that is 35% grape juice. How much of the brand that is 25% grape juice was used?

Answer 1

5.6 gallons.

Explanation:

If we take x gallons of 25% grape juice then it will contain
`(x)/(4)` gallons of pure grape juice.

Again, if we take y gallons of 75% grape juice then it will contain
`(3y)/(4)` gallons of pure grape juice.

If we mix them then the total volume will become x + y = 7 gallons ...... (1)

Again the mixture will become 35% juice.

So,
`((x)/(4) +(3y)/(4) )/(x+y) =(35)/(100)`

⇒ 0.25x + 0.75y = 0.35x + 0.35y

⇒0.1x = 0.4y

⇒x = 4y........ (2)

Now, solving equations (1) and (2) we get, 5y = 7, ⇒ y = 1.4 gallons

Hence, x = 4y = 5.6 gallons

Therefore, the 25% grape juice was mixed by 5.6 gallons. (Answer)