Write a system of equations in x and y and solve.
How much of a 40% antifreeze solution must a mechanic mix with 7% antifreeze solution to have 20 gallons of a 50% anti freeze solution?
(x of 40%) +(y of 7%) = 20 of 50%
40x +7y = 1000 -----------------------(1)
x +y = 20 -----------(2)
Can you solve that now?
You should get
x = 26.06 gal
y = -6.o6 gal
Hey, wait a minute. A negative volume for the 7% antifreeze?
Cannot be.
Umm, the mechanic is trying to get a mixture of 50% from mixing some 40% and some 7%? Cannot be. 50% is both higher than each of the 40% and 7%.
One of the components must be higher than 50%.
So, I think the 7% should be 70%. A typo in your question.
Then
40x +70y = 1000
4x +7y = 100 -----------(1a)
x +y = 20 -------------still (2)
You should get now:
x = 13 and 1/3 gallons
y = 6 and 2/3 gallons