Question

How much of an alloy with 30% copper must be added to 25 pounds of a second alloy which is 20% copper to create a 27% alloy
33.85 lbs.
58.33 lbs.
391.67 lbs.

Answer 1

Answer: 58.33 lbs

Step-by-step explanation:

For Alloy 1:

Let the weight of alloy 1 be “x” pounds.

% of copper present in alloy 1 = 30%

∴ Amount of copper in alloy 1 = 30% of x = 0.3x ….. (i)

For Alloy 2:

The weight of alloy 2 = 25 pounds

% of copper present in alloy 2 = 20%

∴ Amount of copper in alloy 2 = 20% of 25 = (0.2 * 25) ….. (ii)

For Alloy 3:

Here we are given that alloy 1 and alloy 2 are mixed to create a mixture of 27% alloy.

∴ Amount of alloy 3 = 27% of (weight of alloy 1 + weight of alloy 2) = 0.27(x + 25) ….. (iii)

Since alloy 3 is a mixture of (0.3x) of copper in alloy 1 and (0.2*25) of copper in alloy 2, therefore we can write the combined equation from (i), (ii) & (iii) as,

(0.3)(x) + (0.2)(25) = (0.27)(x + 25)

⇒ 0.3x + 5 = 0.27x + 6.75

⇒ 0.03x = 6.75 – 5  

⇒ x = 1.75 / 0.03 = 58.33 pounds or lbs.

Thus, the weight of alloy 1 is 58.33 lbs.