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chiccufrazer1
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

ASIDE: We can eliminate C, D and E immediately (without performing any calculations).
Here's why: If we begin with a mixture that's 60% sugar and then we dilute it by adding water, the resulting mixture will have less than 60% sugar. So, eliminate C, D and E.

Okay, on to the solution.

7.5 liter mixture of water and sugar is 60% sugar.
60% of 7.5 liters is sugar
60% of 7.5 = 4.5, so the 4.5 mixture has 4.5 liters of sugar

1.5 liters of water is added
So, the volume of the new mixture is 9 liters.
Since no sugar was added, the volume of the sugar is still 4.5 liters

(4.5)/9 = 1/2 = 50%
So, the new mixture is 50% sugar.

Answer: B


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chiccufrazer1
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68
If you are used to weighted averages. . .

Water has 0.0 percent sugar, but it is being added

\(.6(7.5) + 0.0(1.5) = \frac{x}{100}(7.5 + 1.5)\)
Both sides * 100:
\(6(75) = 9x\)
\(450 = 9x\)
\(x = 50\) percent

Answer B
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chiccufrazer1
A 7.5 liter mixture of water and sugar is 60% sugar. If 1.5 liters of water is added, approximately what is the % of the new mixture of sugar?

A. 40%
B. 50%
C. 63%
D. 64%
E. 68

Posted from my mobile device

Initial ratio of Water and Sugar \(= 40: 60 = 2: 3\)

Thus, the amount of water \(= \frac{2}{(2+3)} * 7.5 = 3\) liters and the amount of sugar \(= \frac{3}{(2+3)} * 7.5 = 4.5\) liters

Water added \(= 1.5\) liters

Thus, total amount of water and sugar mixture \(= 7.5 + 1.5 = 9\) liters

Percentage of sugar \(= \frac{4.5}{9} = 50\) liters

Correct Answer: Option B


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