How much do brand a (29% fruit juice) must be mixed with a 5 gallon of brand b fruit punch (47% fruit juice) to create a mixture containing 35% fruit juice?

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Explanation:

Let x be the number of gallons for brand A.

Brand A has 29% juice, so 0.29x gallons are pure juice in this container.

Brand B has 47% juice and we have 5 gallons of this, so 0.47*5 = 2.35 gallons of pure juice are in the brand B container.

In total, we have 0.29x+2.35 gallons of juice only

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x is the number of gallons in the brand A container

5 is the number of gallons in the brand B container

x+5 is the total number of gallons of water+juice mix

we want 35% fruit juice, so 35% of (x+5) = 0.35(x+5) is the desired amount of fruit juice we want.

Set this equal to 0.29x+2.35 we found earlier, as this also measures the total amount of fruit juice

Solve for x

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0.35(x+5) = 0.29x+2.35

0.35*x+0.35*5 = 0.29x+2.35

0.35x+1.75 = 0.29x+2.35

0.35x-0.29x = 2.35-1.75

0.06x = 0.6

x = 0.6/0.06

x = 10

The chart shown below might help keep everything organized.

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