Question

How much 10% solution and how much 45% solution should be mixed together to make 100 gallons of 25% solution?

Answer 1

       x + y = 100

0.10x + 0.45 y =25

eliminate

x + y = 100
x  + 4.5 y = 250

-3.5 y = -150
y = 42.85
x = 57.15

hope this helps

Answer 2

Answer:

$V_{1}=57.15\\C_{1}=10%$

$V_{2}=42.85\\C_{2}=45%$

One should use 57.15 galons of 10% solution with 42.85 galons of 45% solution.

Explanation:

$C_{1} *V_{1} =C_{2} *V_{2}$

$V_{1}}+{V_{2}}=100={V_{3}}$

$C_{3}=25%$

${C_{2} =4.5{C_{1}}=45%$

$C_{3} *V_{3} =C_{2} *V_{2} +C_{1} *V_{1}$

$C_{3} =\frac{C_{2} *V_{2} +C_{1} *V_{1}}{V_{3}}$

$C_{3} =\frac{4.5C_{1}(\frac{V_{1}}{4.5} +V_{2})}{V_{3}}$

$\frac{C_{3}*{V_{3}}}{4.5C_{1}}=\frac{V_{1}}{4.5} +V_{2}$

$\frac{C_{3}*{V_{3}}}{4.5C_{1}}=55.55555=\frac{V_{1}}{4.5} +V_{2}$

$V_{2}=100-V_{1}$

$55.55555=\frac{V_{1}}{4.5} +100-V_{1}\\44.4444=V_{1}-\frac{V_{1}}{4.5}\\3.5V_{1}=200\\V_{1}=57.15V_{2}=42.85$