Question

A first alloy contains x pounds of 55% silver. It is mixed with a second alloy containing 30% silver to make 60 pounds of an alloy containing 40% silver. Of the answers listed below, the one closest to the correct value of x is

Answer 1

Answer:

"24 pounds" is the appropriate answer.

Step-by-step explanation:

According to the question, the equation will be:

⇒ $x+y=60$...(equation 1)

or,

⇒ $\frac{55}{100}x+\frac{30}{100}y=\frac{40}{100}\times 60$

      $55x+30y=2400$...(equation 2)

Now,

By multiplying (equation 1) by 55 and (equation 2) by 1, we get

⇒ $55x+55y=3300$...(equation 3)

⇒ $55x+30y=2400$...(equation 4)

From equation 3 and 4, we get

⇒ $25y=900$

       $y=\frac{900}{25}$

          $=36$

By putting the values of "y" in equation 1, we get

⇒ $x=60-36$

       $=24$

Thus the value of x be "24 pounds".