Question

Sarah needs 30 liters of a 25% acid solution how many liters of the 10% and the 30% acid solutions should she mix to get what she needs

Answer 1

Sarah needs 7.5 liters of the 10% acid solution and 22.5 liters of the 30% acid solution.

Explanation:

`x - \text{volume of the}\ 10\%\ \text{acid solution}\\\\30 - x - \text{volume of the}\ 30\%\ \text{acid solution}\\\\p\%=(p)/(100)\\\\25\%=(25)/(100)=0.25,\ 10\%=(10)/(100)=0.1,\ 30\%=(30)/(100)=0.3\\\\25\%\ of\ the\ 30\ liters\to(0.25)(30)\\10\%\ of\ the\ x\ liters\to0.1x\\30\%\ of\ the\ (30-x)\ liters\to0.3(30-x)\\\\\text{The equation:}\\\\0.1x+0.3(30-x)=(0.25)(30)\qquad\text{use the distributive property}\\\\0.1x+(0.3)(30)+(0.3)(-x)=7.5\\\\0.1x+9-0.3x=7.5\qquad\text{subtract 9 from both sides}`

`-0.2x=-1.5\qquad\text{multiply both sides by (-5)}\\\\x=7.5\ (liters)\\\\30-x=30-7.5=22.5\ (liters)`

Answer 2

7.5 L of 10% solution and 22.5 L of 30% solution

Explanation:

Volume of 10% solution plus volume of 30% solution = total volume of 25% volume.

x + y = 30

Acid in 10% solution plus acid in 30% solution = total acid in 25% solution.

0.10 x + 0.30 y = 30 × 0.25

0.10 x + 0.30 y = 7.5

Solve the system of equations, using either substitution or elimination. I'll use substitution:

x = 30 − y

0.10 (30 − y) + 0.30 y = 7.5

3 − 0.10 y + 0.30 y = 7.5

0.20 y = 4.5

y = 22.5

x = 30 − y

x = 7.5

Sarah needs 7.5 L of 10% solution and 22.5 L of 30% solution.