Question

An experiment calls for 5% salt solution. Only a 3% salt solution are available. How many gallons of each must be combined to obtain 30 gallons of 5% salt solution?

Answer 1

Explanation:

Let x be the number of gallons of 3% salt solution needed, and y be the number of gallons of 5% salt solution needed. Then we have the following system of equations:

x + y = 30 (since we need a total of 30 gallons of solution)

0.03x + 0.05y = 0.05(30) (since we need a 5% salt solution)

Simplifying the second equation, we get:

0.03x + 0.05y = 1.5

Multiplying the first equation by 0.03, we get:

0.03x + 0.03y = 0.9

Subtracting this equation from the second equation, we get:

0.02y = 0.6

Dividing both sides by 0.02, we get:

y = 30

So we need 30 gallons of 5% salt solution. Substituting this into the first equation, we get:

x + 30 = 30

So x = 0.

Therefore, we need 0 gallons of 3% salt solution and 30 gallons of 5% salt solution to obtain 30 gallons of 5% salt solution.