Question

you are trying to recreate flubber because you are obsessed with that movie and you thought it was the coolest. you take 70% slime solution and some 40% slime solution to obtain 120 gallons of a 50% slime solution. how much of the 40% slime solution do you need to create your mixture?

a. 40

b. 80

c. 50

d. 70

can you help me solve?

Answer 1

Let $x$ be the amount (gal) of the 40% slime solution you end up using. You want to end up with 120 gal of the 50% solution, so that you would use $120-x$ gal of the 70% solution.

You want the final solution to consist of 50% slime, or 60 gal of slime. Each gal of the 40% solution contributes 0.4 gal of slime, while each gal of the 70% solution contributes 0.7 gal of slime. This means

$0.4x+0.7(120-x)=0.5\cdot120=60$

$\implies0.4x+84-0.7x=60$

$\implies24=0.3x$

$\implies x=80$

so the answer is B.