Question

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

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).

Answer 2

By solving linear equation we got that if 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 then value of x is 11.5

What is linear equation ?

A equation of degree one is known as linear equation.

Here given that 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

So weight of first alloy =2x

weight of second alloy =35-2x

weight of silver in second alloy = (35-2x)(0.15)

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

Now we can write it as

$x+(35-2x)\times0.15=13.3x+5.25-0.3x=13.3\\\\0.7x=13.3-5.25=8.05$

$x=8.05/0.7=11.5$

now

weight of first alloy =2x = 23

weight of second alloy =35-2x =35-23=12

weight of silver in second alloy  = (35-2x)(0.15)=12(0.15)= 1.8

By solving linear equation we got that if 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 then value of x is 11.5

To learn more about linear equation visit : brainly.com/question/14323743