How to calculate?

38175425

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Jun 20, 2020
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"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

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Jun 18, 2007
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"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

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Jan 27, 2012
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6,293
"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
Joined
Jun 20, 2020
Messages
16
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

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Jun 18, 2007
Messages
21,308
(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??
 
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