Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

# Help with algebra? Relevance
• I'm not sure why we'd want to "make a chart,"

but perhaps if I show you an algebraic solution,

your class experience will suggest a suitable chart.

Let a represent the quantity of solution A, in liters,

and b represent the quantity of solution B.

Then we can write the equations

a + b = 4 [describing the total quantity of solution]

and

0.08a + 0.20b = 0.11 (4) [describing the acetic acid percentage]

to represent the problem.

We can simplify that second equation, dividing each side by 0.04 to obtain

2a + 5b = 11

and then find the common solution. Subtracting twice the first equation yields

3b = 3

or

b = 1

3 liters of solution A (contributing 0.24 liters acetic acid)

and

1 liter of solution B (contributing 0.20 liters acetic acid)

to obtain 4 liters of solution with 0.44 liters (11%) acetic acid.

Back to the chart question: Perhaps you could make a table with different quantities of each solution and calculate the acid percentage in each.

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• Let z be the volume of Solution A (in liters) to be found.

Then the volume of Solution B is (4 - z) liters.

(0.08 z) + (0.20 (4 - z)) = 4 (0.11)

Solve for z algebraically:

z = 3 liters Solution A

4 - z = 1 liter Solution B

Make the chart yourself.

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