Question

A 4% peroxide solution is mixed with a 10% peroxide solution, resulting in 100 L of an 8% solution. The table shows the amount of each solution used in the mixture.

Answer 1

33 1/3 L of the 4% solution and 66 2/3 L of the 10% solution.

Explanation:

Let x represent the amount of 4% solution and y represent the amount of 10% solution. Together they make 100 L of solution; this gives us the equation

x + y = 100

x liters of the 4% solution gives us the expression 0.04x.

y liters of the 10% solution gives us the expression 0.10y.

100L of the 8% solution gives us 0.08(100) = 8.

Together this gives us the equation

0.04x+0.10y = 8

This gives us the system of equations

`\left \{ {{x+y=100} \atop {0.04x+0.10y=8}} \right.`

To solve this, we will use elimination. We must make the coefficients of one variable the same; we will make the x coefficients the same by multiplying the first equation by 0.04:

`\left \{ {{0.04(x+y=100)} \atop {0.04x+0.10y=8}} \right. \\\\\left \{ {{0.04x+0.04y=4} \atop {0.04x+0.10y=8}} \right.`

Now we eliminate x by subtracting the second equation from the first one:

`\left \{ {{0.04x+0.04y=4} \atop {-(0.04x+0.10y=8)}} \right. \\\\-0.06y=-4`

Divide both sides by -0.06:

-0.06y/-0.06 = -4/-0.06

y = 66 2/3

Substitute this into the first equation:

x + 66 2/3 = 100

Subtract 66 2/3 from each side:

x + 66 2/3 - 66 2/3 = 100 - 66 2/3

x = 33 1/3

There are 33 1/3 liters of the 4% solution and 66 2/3 liters of the 10% solution.

Answer 2

the 4% amount is 100-x
the 10% amount is x
0.04(100-x)+0.1x=0.08(100)
4-0.04x+0.1x=8
4+0.06x=8
0.06x=4
times 100 both sides
6x=400
divide oth sides by 6
x=66.66
the oher value is
100-x
100-66.6666
33.33333



33.333333L of the 4% solution
66.666666L of the 10% soluution