Filling in the table you have in the right column ...
x × 0.2 = 0.2x
y × 0.05 = 0.05y
and their total
15 × 14% = 2.1
The table tells you two equations based on the totals in the bottom row:
x + y = 15
0.2x + 0.05y = 2.1
There are a number of ways to solve these equations. It often works well to use substitution for mixture problems, substituting for the variable that represents the smallest contributor (y).
0.2x + 0.05(15 - x) = 2.1
0.15x = 1.35 . . . . . . . . simplify and subtract 0.75
x = 9 . . . . . . . . . . . . . . divide by 0.15
y = 15 - 9 = 6
There should be 9 gallons of 20% alcohol in the mix.
There should be 6 gallons of 5% alcohol in the mix.
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I like to use an X-diagram to work mixture problems. The strengths of the contributors to the mix are listed on the left, and the mixture strength is shown in the middle. The numbers on the right are the differences along the diagonals. They tell you the proportion of each contributor to the mix.
Since these proportion numbers add up to 15, the number of gallons of mix you want, each is the number of gallons of the corresponding contributor:
9 gallons of 20%; 6 gallons of 5%.
