SOLUTION: Mr. Costa is filling planter boxes with soil. He has soil that is 23% sand, and he buys 6 pounds of a commercial potting soil that is 39% sand. He mixes some of his soil with the 6

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Question 1156894: Mr. Costa is filling planter boxes with soil. He has soil that is 23% sand, and he buys 6 pounds of a commercial potting soil that is 39% sand. He mixes some of his soil with the 6 pounds of commercial potting soil. The resulting soil mixture is 35% sand. How many pounds of his soil did Mr. Costa use?
[A] 4 lb [B] 2 lb [C] 6 lb [D] 8 lb
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
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MATERIALS CONCENTRATION SAND% QUANT. He Has 23 v Commercial Potting 39 6 Mixture wanted 35 v+6

The description is itself in only one variable.

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Answer by ikleyn(52786)   (Show Source):
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Let H be the amount of his soil of 23% sand. The equation for the mixture 0.23H + 0.39*6 = 0.35*(H + 6). From the equation, express H and calculate H = = 2. ANSWER. He should use 2 pounds of his soil. (Option B)

Answer by greenestamps(13200)   (Show Source):
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Here is a quick non-algebraic way to solve two-part mixture problems like this.

Picture the three percentages on a number line: 23, 35, and 39. The target percentage 35 is 12/16 = 3/4 of the way from 23 to 39.

That means 3/4 of the mixture must be the 39% sand.

So the 6 pounds of 39% sand he is using is 3/4 of the mixture; the 23% sand is 1/4 of the mixture, which is 1/3 of 6 pounds, or 2 pounds.

Answer B