Question

A metal worker has 57 grams of an alloy that is 37% gold. She also has a large supply of an alloy that is 17% gold. How many grams of the 17% gold alloy does she need to add to the 37% gold alloy to obtain an alloy that is 25% gold? Write your answer as a whole number or as a decimal rounded to the nearest tenth.

Answer 1

85.5 grams of 17% gold alloy is added.

Explanation:

A metal worker has 57 grams of an alloy that is 37% gold.

And let x grams of an alloy which is 17% gold.

Let's add them to get 25% of (x+57)grams of alloy.

So, we can set up equation as

57(37%) +x(17%) =(x+57)(25%)

Simplify and solve the equation for x.

21.09+0.17 x= 0.25 x+14.25

Subtract both sides 0.25 x

21.09-0.08 x =14.25

Subtract both sides 19.95

-0.08 x=-6.84

Divide both sides by -0.08

x=85.5 grams