8th grade honors math

Question

A metalworker has a metal alloy that is 30​% copper and another alloy that is 65​% copper. How many kilograms of each alloy should the metalworker combine to create 50 kg of a 51​% copper​ alloy?

Answer 1

Answer: 20kg (30% Cu) and 30kg (65% Cu) for 51% Cu 50kg alloy

Set up two equations as following:

1) (0.3x + 0.65y)/50 = 0.51

Multiply both sides by 50 => 0.3x + 0.65y = 25.5

Multiply both sides by 10 (easier numbers) => 3x + 6.5y = 255

2) x+ y = 50

Multiply both sides by 3 = 3x + 3y = 150

Set up both equations as following:

3x+6.5y = 255

3x+3y = 150

Solve for y by dividing by 3.5 => 3.5y = 105

y= 30 (kg)

Plug back into any equation and solve for x.

x+ 30 = 50

x = 20 (kg)

Good luck, Natalie, and let me know if you have any questions!