# How to calculate?

#### 38175425

##### New member
"A 20-gallon alcohol-water solution contains 15% pure alcohol. How much alcohol should be added to make a new solution that is 20% alcohol?"

My calculation:
20 x 15/100 = 3
20 x 20/100 = 4
1-gallon alcohol should be added to make a new solution that is 20% alcohol.

#### Subhotosh Khan

##### Super Moderator
Staff member
"A 20-gallon alcohol-water solution contains 15% pure alcohol. How much alcohol should be added to make a new solution that is 20% alcohol?"

My calculation:
20 x 15/100 = 3
20 x 20/100 = 4
1-gallon alcohol should be added to make a new solution that is 20% alcohol. .....................Incorrect
Assume that we have to add 'x' gallons of alcohol (to the 15% solution)

Volume of alcohol in original solution = 0.15 * 20 = 3 gallons

New volume of mixture = 20 + x

Volume of alcohol in final solution = 3 +x

given: new solution that is 20% alcohol

So:

(3 + x)/(20 + x) = 20% = 0.2

Solve for 'x'

#### HallsofIvy

##### Elite Member
"A 20-gallon alcohol-water solution contains 15% pure alcohol. How much alcohol should be added to make a new solution that is 20% alcohol?"

My calculation:
20 x 15/100 = 3
20 x 20/100 = 4
1-gallon alcohol should be added to make a new solution that is 20% alcohol.
Could you explain why you did those calculations? Yes, 15% of 20 gallons is 20 x 15/100= 3 gallons of alcohol. But after you add alcohol the solution will no longer be 20 gallons! In particular, if you add one gallon of alcohol you will have 21 gallons of solution, not 20! 4 gallons of alcohol in 21 gallons of solution is 4/21= 0.19047 so the solution is now 19.4% alcohol, not 20%!

If you add x gallons you will have 3+ x gallons of alcohol in 20+ x gallons of solution. You want $$\displaystyle \frac{3+ x}{20+ x}= 0.20$$.

#### 38175425

##### New member
Assume that we have to add 'x' gallons of alcohol (to the 15% solution)

Volume of alcohol in original solution = 0.15 * 20 = 3 gallons

New volume of mixture = 20 + x

Volume of alcohol in final solution = 3 +x

given: new solution that is 20% alcohol

So:

(3 + x)/(20 + x) = 20% = 0.2

Solve for 'x'
(3 + x)/(20 + x) = 20% = 0.2
3 + x = 0.2(20 + x)
3 + x = 4 + 0.2x
15 + 5x = 20 + x
-5 + 5x = x
-5 = - 4x
4x = 5
x = 1.25

#### Subhotosh Khan

##### Super Moderator
Staff member
(3 + x)/(20 + x) = 20% = 0.2
3 + x = 0.2(20 + x)
3 + x = 4 + 0.2x
15 + 5x = 20 + x
-5 + 5x = x
-5 = - 4x
4x = 5
x = 1.25
Almost good work!

x = 1.25 ....... number is correct - but what is the unit? ft3, gallons, kg, lb, horses, elephants .....what??