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1. A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture?

(A) 1.6 ounce (B) 3.2 ounce © 4.8 ounce (D) 6.4 ounce (E) 8 ounces

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B. 3.2 Ounce

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1. A full glass of juice is a mixture of 20% grape juice and 80% apple juice. The contents of the glass are poured into a pitcher that is 200 percent larger than the glass. The remainder of the pitcher is filled with 16 ounces of water. What was the original volume of grape juice in the mixture?

(A) 1.6 ounce

(B) 3.2 ounce

(D) 6.4 ounce

(E) 8 ounces

The contents of the glass are poured into a pitcher that is 200 percent larger than the glass.

Be careful here. Many people incorrectly interpret this as "the pitcher holds twice as much as the glass does." This interpretation is incorrect. The pitcher actually holds THREE TIMES as much as the glass does.

For example, if the glass holds 5 gallons, then 200% of 5 = 10. So, the pitcher holds 10 gallons MORE than the glass does. In other words, the pitcher holds 15 gallons.

Okay, now back to the question.

When we pour the glass of juice into the pitcher, the pitcher is now 1/3 full (since the pitcher holds THREE TIMES as much as the glass does)

In other words, the pitcher is presently 2/3 EMPTY.

The remainder of the pitcher is filled with 16 ounces of water.

Ah, so 16 ounces fills up the remaining 2/3 of the pitcher (which was formerly empty)

If 16 ounces = 2/3 of the pitcher's volume, then 8 ounces = 1/3 of the pitcher's volume.

Well, the volume of the GLASS = 1/3 of the pitcher's volume, so the GLASS must hold 8 ounces of juice.

If the glass holds 8 ounces of juice, and 20% of the liquid is grape juice, then the volume of grape juice in the glass = 20% of 8 ounces = 1.6 ounces.

Cheers,

Brent

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