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dr.loube, a chemist, mixes two solutions. one is 24% acid ( the rest is water) and the other is 41% acid. about how much of each solution does she need to produce 50 gallons of a solution that is 31% acid?

Sagot :

fichoh

Using a system of equations, the amount of solution a and b required to make the required gallons of the solution are 29.41 and 20.59 respectively.

Let :

  • Solution with 24% acid = a
  • Solution with 41% acid = b

a + b = 50 - - - - (1)

0.24a + 0.41b = 50 × 0.31

0.24a + 0.41b = 15.5 - - - - (2)

From (1) :

a = 50 - b - - - - (3)

Substituting (3) into (2)

0.24(50 - b) + 0.41b = 15.5

12 - 0.24b + 0.41b = 15.5

0.17b = 15.5 - 12

0.17b = 3.5

b = 20.588

From (3) :

a = 50 - 20.588

a = 29.412

Therefore, about 29.41 gallons of solution a and 20.59 gallons of solution b is required.

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