# If you mix 150 grams of a 22% sugar solution and 250 grams of a 16% sugar solution, what percent of the mixture is sugar?

Jun 6, 2014

The mass percent of the sugar is 18.2 %.

Percent by mass is the mass of the solute divided by the mass of the solution, multiplied by 100.

% by mass = $\left(\text{mass of solute")/("mass of solution}\right)$ × 100 %

Step 1 — Determine the mass of the solute.

We must find the mass of sugar in each solution.

In the 22 % solution:

Mass of sugar = 150 g solution × $\left(22 \text{g sugar")/(100"g solution}\right)$ = 33 g sugar

In the 16 % solution:

Mass of sugar = 250 g solution × $\left(16 \text{g sugar")/(100"g solution}\right)$ = 40 g sugar

Total mass of sugar = 33 g + 40 g = 73 g

Step 2 — Determine the mass of solution.

The total mass of the two solutions is 150 g + 250 g = 400 g

Step 3 — Determine the percent by mass of the sugar.

% by mass = $\left(\text{mass of sugar")/("mass of solution}\right)$ × 100 % = $\left(73 \text{g")/(400"g}\right)$ × 100 % = 18.2 %

The mass percent of the sugar is 18.2 %.