Question

a chemist needs to mix up 50 gallons of a 60% acid solution. she only has 50% and 75% solutions on hand. how many gallons should she mix together?

Answer 1

Solution:-

Given that, a chemist has only 50% and 75% solutions on hand. She needs to mix up 50 gallons of a 60% acid solution.

We have to determine the number of gallons she should mix together inorder to obtain 50 gallons of a 60% acid solution.

Let,

= gallons of the 50% solution

T

= gallons of the 75% solution

The total volume of the new mixture is 50 gallons.

Therefore,

I + y = 50 ....equation(1)

According to question,

Each gallon of 50% solution contributes 0.5 gallon of acid, and each gallon of the 75% solution contributes 0.75 gallon of acid. The final mixture needs to have a concentration of 60% acid.

Hence,

0.5.0 + 0.75y = 0.6 x 50

$x+y=50$

$0.5\times (50)-0.5\times (y)+0.75y = 30$

$y = \frac{5}{0.25}$

$\boldsymbol{y = 20}\; \; gallons$

$\boldsymbol{x= 30}\; \; gallons$

Hence,

She should mix $\boldsymbol{30}$ gallons of the 50% solution and $\boldsymbol{20}$ gallons of the 75% solution.