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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.
