A metalworker has a metal alloy that is 30% copper another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 90kg of a 62% copper alloy

Answer 1

30 % = 30 / 100 = 0.3

70 % = 70 / 100 = 0.7

62 % = 62 / 100 = 0.62

x = the amount of 30% alloy

y = the amount of 70% alloy

x + y = 90

y = 90 - x

So:

0.3 ∙ x + 0.7 ∙ y = 0.62 ∙ 90

0.3 ∙ x + 0.7 ∙ ( 90 - x ) = 0.62 ∙ 90

0.3 ∙ x + 0.7 ∙ 90 - 0.7 ∙ x = 0.62 ∙ 90

0.3 ∙ x + 63 - 0.7 ∙ x = 55.8

- 0.4 x + 63 = 55.8

Subtract 63 to both sides

- 0.4 x = - 7.2

Divide both sides by - 0.4

x = 18

y = 90 - x = 90 - 18 = 72

18 kg at 30%

72 kg at 70%