Question

donna has 40 ounces of an alloy containing 65% iron. How many ounces of a second alloy that is 42% iron should be mixed with the first alloy to get a new alloy this is 50% iron

Answer 1

40 oz of a 65% iron alloy contains 40 × 0.65 = 26 oz of iron.

x oz of a 42% alloy contains 0.42x oz of iron.

To end up with an alloy of 50% iron, Donna needs to use x oz of the 42% alloy such that

(26 + 0.42x) / (40 + x) = 0.50

Solve for x :

26 + 0.42x = 0.50 (40 + x)

26 + 0.42x = 20 + 0.50x

6 = 0.08x

x = 75