How many oz. of pure gold must be added to 5 oz. of something that is 1 % gold so that the mixture is 6% gold?

Answer 1

Careful this is a trick question since you'll be adding weight and the end result will have the mixture = more then 5 oz's.
5 * .01 = .05 oz of gold already in the mixture.

Your equation will look something like this
1% * 5oz + N oz = 6% * (5oz + N oz)

Convert it into calculable numbers:
.01 * 5 + N = .06 *(5 + N)

Get N, which is the ounces of gold you need to add to the mixture onto one side:
N - .06(5+N) = -(.01*5)
N - .06*5 - .06*N = -.05
N - .3 - .06N = -.05
N - .06N = .25

Subtract N - .06N = .94N
So
.94N = .25

Divide by .94
.94N / .94 = .25/.94
And you get
N = .26595745.. oz

So you need to add about 2.6595745 oz of pure gold to the mixture.

Answer 2

X oz. of 100% gold + 5 oz. of 1% gold = (X + 5) oz. of 6% gold

Thus, 100*X + 5*1 = 6(X + 5)

100X + 5 = 6X + 30

94X = 25

X = 25 / 94 oz., which is approximately 0.266 oz.