Math help for school

Question

1) A radiator hold 5 gallons . how much of 30 percent antifreeze solution should be drained and replaced with pure water to reduce the solution to 15 percent antifreeze.

2) Gabe a nuclear physicist needs 80 liters of 30 percent acid solution he has 20 percent solution and 60 percent solution. How many liters of each does he need to make the needed 80 liters of 30 percent acid solution.

Answer 1

All the amounts must refer to the water.

If the original solution is 30% antifreeze, then 70% is water

70%(5 - x) + 100%x = 85%(5)

0.7(5 - x) + x = 0.85(5)

3.5 - 0.7x + x = 4.25

3.5 + 0.3x = 4.25

0.3x = 0.75

x = 2.5

 

Two and one-half gallons should be replaced.

Answer 2

2)

Let x be quantity of 20% alcohol

Let y be quantity of 60% alcohol

x+y=80

.2x+.6y=.3(80)

 

x+y=80

2x+6y=240

 

x+y=80

x+3y=120

 

2y=40

y=20

x=60