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Suppose G gallons are used.

Before mixing, you have

5*65 + G*120 = 325 + 120G gallon-degrees.

After mixing, you have

(5+G)*70 gallon-degrees

So 325 + 120G = (5+G)*70 = 350 + 70G

So 50G = 25

G = 0.5 gallons.

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Q: How many gallons of 120 degree water would it take to raise 5 gallons of 65 degree water to 70 degrees?
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