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You have enough information to obtain two equations. 1. You know that when the two liquids are added together, you need 400L total. 2. You also know that the 80% acid times its volume plus 30% acid times its volume must equal 62% times the 400L. 3. Write the two equations. Let x = volume 80% acid & y = volume 30% acid. Therefore from (1) above: x + y = 400; equation A From (2) above: .8x + .3y = .62*400; equation B 4. You have two equations, two unknowns. Solve for x & y. 5. Multiply equation A by -.8 and add equations A & B. Note x adds out to 0. Equation A now becomes -.8x - .8y = -.8*400 or -.8x - .8y = -320. -.8x - .8y = -320 +.8x + .3y = 248 (note .62*400 = 248) So -.5y = -72 and divide both sides by -.5 which yields y = 144. 6. Use equation A to solve for x since we now know "y"; x + 144 = 400 or x = 256. 7. Answer: 256L of 80% acid & 144L of 30% acid.

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Q: A chemist has one solution that is 80 percent acid and another solution that is 30 percent acid how much of the second 30 percent solution is needed to make a 400L solution that is 62 percent acid?
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