A first alloy contains $x$ pounds of 50% silver. it is mixed with a second alloy containing 15% silver to make 35 pounds of an alloy containing 38% silver. of the answers listed below, the one closest to the correct value of $x$ is

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Mathematics

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15 November, 17:53

A first alloy contains $x$ pounds of 50% silver. it is mixed with a second alloy containing 15% silver to make 35 pounds of an alloy containing 38% silver. of the answers listed below, the one closest to the correct value of $x$ is

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Trenton Taylor · Answer 1

Let first alloy contains x pounds of silver, which is 50% of full weight, then the weight of first alloy is 2x.

The second alloy has weight 35-2x pounds and contains 15% silver, then weight of silver in this alloy is (35-2x) * 0.15 pounds.

35 pounds of mixed alloy contains 38% silver, that is 35*0.38=13.3 pounds.

If you add the weights of silver from two alloys you obtain the weight 13.3 pounds (the weight of silver in mixed alloy). x + (35-2x) * 0.15=13.3x+5.25-0.3x=13.3

0.7x=13.3-5.25=8.05

x=8.05:0.7=11.5 pounds (silver content in the first alloy) and 2x=23 pounds is the weight of first alloy.

35-23=12 pounds is the weight of second alloy and 12*0.15=1.8 pounds (silver content in the second alloy).