Question

A company is making detergent out of soap and water. They made one batch that has 30% soap and another batch which is 60% soap. If they mix 600 liters of the first batch with 300 liters of the second batch, what percent of soap will be in the detergent?

Answer 1

The amounts of the 1st and 2nd solution, will be 300 + 600, or 900 liters
the amount of pure soap in the solution will be (0.30)(600)+(0.60)(300)

thus whatever (0.30)(600)+(0.60)(300) is, must equal 900x, since that's how much pure soap the mixture of 900liters has


$\bf \begin{array}{lccclll} &amount&soap&\textit{amount of soap}\\ &-----&-----&--------\\ \textit{first solution}&600&0.30&(0.30)(600)\\ \textit{second solution}&300&0.60&(0.60)(300)\\ -----&-----&-----&--------\\ mixture&900&x&(900)(x) \end{array}\\\\ -----------------------------\\\\ (0.30)(600)+(0.60)(300)=(900)(x)$

solve for "x"