Mixes, systems of equations?

Question

The density of a penny is 8.56 g/ml. If the density of copper is 8.96 g/ml, and the density of zinc is 7.14, what percent of the penny is copper? What percent is zinc?

Answer 1

Let's assume we have one g of a penny and solve for percent by mass:

gramsCu + gramsZn = 1 gram
gramsZn = 1 - gramsCu
1/8.56 ml = (1/8.96) ml/g*(gramsCu) + (1/7.14) ml/g *(gramsZn)
1/8.56 ml = (1/8.96) ml/g*(gramsCu) +(1/7.14) ml/g *(1 -gramsCu)
1/8.56 = 1/8.96 *(Cu) + 7.14*(1 - Cu)
1/8.56 = 1/8.96 *(Cu) + 7.14*(1 - Cu)
0.117 = 0.112Cu + 0.14(1-Cu)
0.117 = 0.112Cu + 0.14- 0.14Cu
0.117 - 0.14 = 0.112Cu - 0.14Cu
0.023 = 0. 028 Cu
0.82 g Cu
0.82 grams copper out of 1 gram of penny
therefore 82% of the penny is copper
and 18% is zinc

Answer 2

Let z = the percentage of the penny made by zinc.

z(7.14) + (1-z)(8.96) = 8.56

Then solve for z; subtract from 100% to find the portion made by copper.