SOLUTION: An alloy is composed of the following: An amount of copper. An amount of nickel equal to 62.5% of the copper. An amount of zinc equal to 33.3% of the copper. An amount

Question 1162242: An alloy is composed of the following:
An amount of copper.
An amount of nickel equal to 62.5% of the copper.
An amount of zinc equal to 33.3% of the copper.
An amount of lead equal to 5% of the copper.
The total alloy weighs 40 1/6 lbs.
Determine amount of each part.
Unsure how to solve.
Found 2 solutions by greenestamps, Boreal:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Let x be the amount (pounds) of copper.

Then express the amount of each other element in terms of x.

nickel: 62.5% of x, which is (5/8)x
zinc: 33.3% of x, which is (presumably) (1/3)x
lead: 5% of x, which is (1/20)x

The total weight is 40 1/6 pounds, or (241/6) pounds:

Multiply through by the least common denominator, which is 120:

ANSWERS:

copper: x = 20 pounds
nickel: (5/8)x = 12 1/2 pounds
zinc: (1/3)x = 6 2/3 pounds
lead: (1/20)x = 1 pound

CHECK:
20 + 12 1/2 + 6 2/3 + 1 = 39+3/6+2/6 = 40 + 1/6

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
A couple of ways to go about it
Can let copper=x and the other small fractions of x
or let copper=24x. The 24x is not magic, but it is small enough and easily divisible by the other percentages with the exception of lead. I could have made it 120x, then nickel would have been 75x, copper 40x, lead 6x. I just thought of working with smaller numbers, that is all.
Nickel is 5/8 of that or 15x
Zinc is 1/3 of that or 8x
Lead is 1/20th or it or 1.2x
The total is 48.2x, and it equals 40 1/6=40.166 lb
putting both in fractional form, 48 1/5x=40 1/6x
x=40 1/6/(241/5)=(241/6)*(5/241); the 241 s cancel and x=(5/6) lb.
That makes
lead 1 lb.
zinc 6 2/3 lb
nickel 12 1/2 lb
and copper 20 lb
They add to 40 (1/6) lb.
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