How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid?

Answer 1

Hi Xandra,

The best thing to do with word problems is identify what is given (known), not given (unknown) and then translate the English into math!

Unknown - How much of the 60% solution we need. Let's call it x

Known - We have 50 gallons of the 24% solution.

Since percentages are just the number given divided by 100 we'll use .60 to represent the 60% solution and .24 to represent the 24% solution and .50 to represent the 50% solution.

The total we have of both solutions is x + 50

So we need:

.60(amount of 60% solution) + .24(amount of 24% solution) = .50 (total amount of solution)

.60 (x) + .24 (50) = .50(x + 50)

.6x + 12 = .5x + 25 - multiply and distribute

.1x = 13 - combine like terms

x = 130 - divide both sides by .1

So we need 130 gallons of the 60% solution! You can substitute 130 back in for x and check it.

Answer 2

Let x be gallons of 60% solution. Then 0.60x+0.24(50)=0.50(x+50). Solve this for x. 0.60x+12=0.50x+25. so 0.10x=13 and x=130 gallons of 50% solution.

Answer 3

130 gallons of 60% solution must be mixed with 50 gallons of 24% acid to obtain a solution that is 50% acid.

Here is how:

We already know that the final product will include 50 gallons of 24% acid. We just do not know how much 60% solution we need! Let's call this unknown amount of 60% solution X. So, we need X gallons of 60% solution and 50 gallons of 24% solution to give us the 50% solution mix in the end.

So now, we know that X + 50 = total gallon of acid we will have in the end because X is how much of 60% that we are combining with the 50 gallons of 24%.

From this information we can set up the following equation:

0.6(X) + 0.24(50) = 0.5(X + 50)

Recall that a percentage is a number over 100, so 60% = 60/100 = 0.6

Also recall by multiplying the percentage by the number of gallons we are getting the concentration of the solution.

Also note that 0.5(X + 50) is the total concentration in the end from mixing the 2 acids.

Okay, so now we have an algebraic expression to solve!

0.6(X) + 0.24(50) = 0.5(X + 50)

0.6(X) + 12 = 0.5X + 25

0.1(X) = 13

X = 130 gallons

So, we need 130 gallons of 60% acid solution to combine to make our final product.