Mixtures, Distance System of Equations

Question

You need 420 mL of a 50% alcohol solution. On hand, you have 45% alcohol mixture. You also have 75% alcohol mixture. How much of each mixture will you need to add to obtain the desired solution?

You will need ____ mL of the 45% solution

You will need ____mL of the 75% solution

Answer 1

Let x = the amount of 45% alcohol solution and y = the amount of the 75% alcohol solution.

.45x + .75y = .50(420)=210

x+y = 420

y=420-x

.45x + .75(420-x) =210

.45x +315 -.75x = 210

-.30x = - 105

x = 350 mL

y = 420-350 = 70 mL

You will need 350 mL of the 45% solution

You will need 70 mL of the 75% solution