Question

A goldsmith mixes 5oz of a 30% gold alloy with 20oz of a 15% gold alloy. What is the percent concentration of the resulting alloy?

Answer 1

Since we mix 5 oz of 30% with 20 oz of 15%, then

Let us add 5 x 30% and 20 x 15%

`\begin{gathered} 5*(30)/(100)+20*(15)/(100)= \\ \\ (150)/(100)+(300)/(100)= \\ \\ 1.5+3= \\ 4.5\text{ oz} \end{gathered}`

This 4.5 oz has x concentration of the total amount 5 oz and 20 oz, then

we will multiply x by (5 + 20) and equate the answer by 4.5

`\begin{gathered} (5+20)x=4.5 \\ 25x=4.5 \end{gathered}`

Divide both sides by 25

`\begin{gathered} (25x)/(25)=(4.5)/(25) \\ x=(9)/(50) \end{gathered}`

Change it to percent by multiplying it by 100%

`\begin{gathered} x=(9)/(50)*100\text{ \%} \\ x=18\text{ \%} \end{gathered}`

The percent of concentration is 18%