System of equations

Question

2. How many ounces of a 10% acid solution should be mixed with a 50% acid solution to get 120 ounces of a 20% acid solution. Write the system of equations that would be used to solve this.

Be sure to label what your variables represent.

Answer 1

Hi Guadalupe L

90 ozs of 10%

30 ozs of 50%

A system using substitution would work for this solution

Let x = the amount of the 50% solution

Let y = the amount of the 10% solution

We are given a total volume of 120 oz at a final concentration of 20%

Equation 1 is for total volume

x + y = 120

y = 120 - x

Equation 2 is for the final concentration

0.5x + 0.1y = .2(120) = 24

Substitution y in Equation 2 we have

0.5x + 0.1(120 - x) = 24

0.5x + 12 - 0.1x = 24

Combining like terms

0.5x - 0.1x + 12 = 24

0.4x + 12 = 24

Subtract 12 from both sides of the equation

0.4x = 12

Divide both sides by 0.4

x = 30

y = 120 - x = 120 - 30 = 90

Checking

0.5(30) + 0.1(90) = 24

15 + 9 = 24

Hope this helps