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

"24 pounds" is the appropriate answer.

Explanation:

According to the question, the equation will be:

⇒
`x+y=60`...(equation 1)

or,

⇒
`(55)/(100)x+(30)/(100)y=(40)/(100)* 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=(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".