Question

For the given word problem, write a system of equations, clearly define any variables, and show work for full credit.

A photographer is mixing 5% acetic acid solution with a 10% acetic acid solution to get two liters of a 7% solution.
How many liters of each solution should he add?

Answer 1

The 100 always go on the button and the % go on top so the answer is 53%(44*%34)

Answer 2

Let x be the amount (in liters) of the 5% acetic acid solution to be added.

Let y be the amount (in liters) of the 10% acetic acid solution to be added.

The system of equations is:

x + y = 2 (the total amount of solution is 2 liters)

0.05x + 0.10y = 0.07(2) (the amount of pure acetic acid in the final solution is 7% of 2 liters)

Simplifying the second equation:

0.05x + 0.10y = 0.14

5x + 10y = 14 (multiplying both sides by 100)

We now have a system of two equations with two variables. We can solve it by substitution or elimination. Here, we'll use substitution:

x + y = 2 => x = 2 - y (subtracting y from both sides)

Substituting x in the second equation:

5(2 - y) + 10y = 14 (replacing x by 2 - y)

10 - 5y + 10y = 14

5y = 4

y = 0.8

So the photographer should add 0.8 liters of the 10% acetic acid solution and 2 - 0.8 = 1.2 liters of the 5% acetic acid solution. We can check that this solution satisfies both equations:

0.05(1.2) + 0.10(0.8) = 0.06 + 0.08 = 0.14

1.2 + 0.8 = 2

Therefore, the answer is:

The photographer should add 0.8 liters of the 10% acetic acid solution and 1.2 liters of the 5% acetic acid solution.