Algebra Problem Help?

ctccb

Suppose that you have a supply of a 25% solution of alcohol and a 75% solution of alcohol. How many quarts of each should be mixed to produce 50 quarts that is 40% alcohol?

25% solution________________qt

75% solution _______________ qt

Thank you for helping me!

seamus-o

Let number of qt 25% solution = x

and let number of qt 75% solution = y

0.25x + 0.75y = 0.4 x 50

0.25x + 0.75y = 20 ... [eqn 1]

x + y = 50

y = 50 - x ... [eqn 2]

Subs [eqn 2] into [eqn 1] → 0.25x + 0.75(50 - x) = 20

0.25x + 37.5 - 0.75x = 20

0.5x = 17.5

x = 35

subs x = 35 into [eqn 2] → y = 50 - 35

y = 15

so 35 qt 25% solution and 15 qt 75% solution should be mixed for the required 40% solution