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

`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.

Step-by-step 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) =(C_(2) *V_(2) +C_(1) *V_(1))/(V_(3))`

`C_(3) =(4.5C_(1)((V_(1))/(4.5) +V_(2)))/(V_(3))`

`\frac{C_(3)*{V_(3)}}{4.5C_(1)}=(V_(1))/(4.5) +V_(2)`

`\frac{C_(3)*{V_(3)}}{4.5C_(1)}=55.55555=(V_(1))/(4.5) +V_(2)`

`V_(2)=100-V_(1)`

`55.55555=(V_(1))/(4.5) +100-V_(1)\\44.4444=V_(1)-(V_(1))/(4.5)\\3.5V_(1)=200\\V_(1)=57.15V_(2)=42.85`