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A 2% solution of acid was mixed with a 12% solution to produce an 8% solution. The amount of 2% solutions is 2 liters less than the 12% solution. How much 2% solution and how much 12% solution were used to produce 10L of the 8% solution ?

Answer :

Answer:

The number of liters of 2% solution of acid = x = 4 Liters

The number of liters of 12% solution = y = 6 Liters

Step-by-step explanation:

Let us represent

The number of liters of 2% solution of acid = x

The number of liters of 12% solution = y

The system of equations for the above question is given as:

x + y = 10L...... Equation 1

x = 10 - y

2% × x + 12% × y = 8% × 10L

0.02x + 0.12y = 0.8....... Equation 2

We substitute 10 - y for x in Equation 2

0.02(10 - y) + 0.12y = 0.8

0.2 - 0.02y + 0.12y = 0.8

Collect like terms

- 0.02y + 0.12y = 0.8 - 0.2

0.10y = 0.6

y = 0.6/0.10

y = 6 Liters = 6 L

Note that:

x = 10 - y

x = 10 - 6

x = 4 Liter= 4 L

Therefore:

The number of liters of 2% solution of acid = x = 4 Liters

The number of liters of 12% solution = y = 6 Liters

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