Math problem help?

Question

How much pure acid should be mixed with 3 gallons of a 50% acid solution in order to get an 80% acid solution?

7.5 gal
4.5 gal
12 gal
1.5 gal

Answer 1

Let X be the number of gallons to add:

You have a 50% solution (3 gallons)
You are adding a 100% solution (X gallons)
That should result in an 80% solution (3 + X gallons)

As an equation:
50% * 3 + 100% * X = 80%* (3 + X)

Multiply everything by 100 to get rid of percents:
150 + 100X = 80(3 + X)

Distribute the 80 through on the right:
150 + 100X = 240 + 80X

Subtract 80X from both sides:
150 + 20X = 240

Subtract 150 from both sides:
20X = 240 - 150
20X = 90

Now divide by 20:
X = 90/20
X = 9/2
X = 4½

So you need to add 4½ gallons of pure acid.

Answer:
B) 4.5 gallons

Answer 2

4.5 it is a the amount need can be found by ((3*80)/50)-3