Question: Computing a percent mixture An alloy is a mixture of metals. Suppose that a certain alloy is made…

Computing a percent mixture

An alloy is a mixture of metals. Suppose that a certain alloy is made by mixing 28 grams of an alloy containing 15% copper with 100 grams of an alloy containing 55% copper.

Answer the questions below. Do not do any rounding.

(a) How many grams of copper are in the resulting mixture?

grams

(b) What percentage of the resulting mixture is copper?

%

Solution

To solve the problem, we’ll go through each part step by step. (a) How many grams of copper are in the resulting mixture? First, calculate the amount of copper in each alloy. For the 28 grams of alloy containing 15% copper: \[ 28 \times 0.15 = 4.2 \text{ grams} \] For the 100 grams of alloy containing 55% copper: \[ 100 \times 0.55 = 55 \text{ grams} \] Add these amounts to find the total grams of copper in the mixture: \[ 4.2 + 55 = 59.2 \text{ grams} \] (b) What percentage of the resulting mixture is copper? First, find the total weight of the mixture: \[ 28 + 100 = 128 \text{ grams} \] Calculate the percentage of copper in the mixture: \[ \frac{59.2}{128} \times 100 = 46.25\% \] Therefore, the mixture contains 59.2 grams of copper, and the percentage of copper is 46.25%.