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Sindrei [870]
3 years ago
11

A metalworker has a metal alloy that is 15​% copper and another alloy that is 75​% copper. How many kilograms of each alloy shou

ld the metalworker combine to create 120 kg of a 51​% copper​ alloy?
Mathematics
1 answer:
lisov135 [29]3 years ago
4 0

48 kilograms of 15 % copper is combined with 72 kilograms of 75 % copper to create 120 kg of a 51​% copper​ alloy

<em><u>Solution:</u></em>

Let "x" be the kilograms of 15 % copper

Then, (120 - x) be the kilograms of 75 % copper

Then, according to question,

"x" kilograms of 15 % copper is combined with (120 - x) kilograms of 75 % copper to create 120 kg of a 51​% copper​ alloy

Thus we frame a equation as:

15 % of x + 75 % of (120 - x) = 51 % of 120

<em><u>Solve the equation for "x"</u></em>

15 \% \times x + 75 \% \times (120-x) = 51 \% \times 120\\\\\frac{15}{100} \times x + \frac{75}{100} \times (120-x) = \frac{51}{100} \times 120\\\\0.15x + 0.75(120-x) = 0.51 \times 120\\\\0.15x + 90 - 0.75x = 61.2\\\\0.6x = 90 - 61.2\\\\0.6x = 28.8\\\\Divide\ both\ sides\ by\ 0.6\\\\x = 48

Thus 48 kilograms of 15 % copper used

Then, (120 - x) = (120 - 48) = 72

Thus, 72 kilograms of 75 % copper is used

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