MATH SOLVE

2 months ago

Q:
# Serena is making an experiment. For that, she needs 20 grams of a 52% solution of salt. She has two large bottles of salt water: one with 40% and the other with 70% of salt in them. How much of each must she use to make the solution she needs?

Accepted Solution

A:

x + y = 20 --> eqn 1

The second equation would be the mass balance shown below:

(x)(0.40) + y(0.70) = 20(0.52) --> eqn 2

Rearranging eqn 1,x = 20 - ySubstitute this to eqn 2:

(20 - y)(0.40) + y(0.70) = 20(0.52)Solve for y,y = 8 grams Finally, solve for x.x = 20 - 8 = 12 grams

Therefore, Serena needs 12 grams of the 40% solution and 8 grams of the 70% solution.

The second equation would be the mass balance shown below:

(x)(0.40) + y(0.70) = 20(0.52) --> eqn 2

Rearranging eqn 1,x = 20 - ySubstitute this to eqn 2:

(20 - y)(0.40) + y(0.70) = 20(0.52)Solve for y,y = 8 grams Finally, solve for x.x = 20 - 8 = 12 grams

Therefore, Serena needs 12 grams of the 40% solution and 8 grams of the 70% solution.