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| Math Central | Quandaries & Queries |
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Question from Nathan, a student: How many gallons of 60% solution must be added to 40 gallons of a 10% solution to produce a 20% solution? |
Hi Nathan,
You have 40 gallons of a 10% solution of some compound so the amount of this compound in the solution is 0.10 × 40 = 4 gallons. Suppose you add x gallons of a 60% solution then the amount of the compound you are adding is 0.6 × x gallons.
I put this information in a table
| Volume of solution | Percentage compound | Volume of compound | |
|---|---|---|---|
| 40 gallons | 10% | 4 gallons | |
| x gallons | 60% | 0.6 × x gallons | |
| Total | 40 + x gallons | 20% | 4 + 0.6 × x gallons |
If 20% of (40 + x) gallons is (4 + 0.6 × x) gallons, what is x? Make sure you check your answer.
Penny
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