Please Help this is killing me right now. I know how to solve this word problem once it is set up, but I just don't know how to set it up.

The radiator of a car needs to contain 40 liters of 40% anti freeze. The radiator now contains 40 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze to get the desired strength?

Question

Please Help this is killing me right now. I know how to solve this word problem once it is set up, but I just don't know how to set it up.

The radiator of a car needs to contain 40 liters of 40% anti freeze. The radiator now contains 40 liters of 20% antifreeze. How many liters of this solution must be drained and replaced with 100% antifreeze to get the desired strength?

amistre64 · Answer

amount(%)  is the key to this stuff:

x+y = 40;   y = 40-x
...................................
replace the y with its 'value' from above and solve for x
x(.2) + y(1) = 40(.4)

amistre64 · Answer

makes sense?

anonymous · Answer

so 30 liters? 30 liters must stay so 10 liters need to be drained?

amistre64 · Answer

dunno; let me do the math :)

anonymous · Answer

okay haha

anonymous · Answer

This problem is haunting my life right now. It's the devil...

amistre64 · Answer

.2x + 40 - x = 16

.2x - x = 16-40

-.8x = -24

x = 24/.8 = 240/8 = 30

there should be 30 liters of 20% so we need to drain 10 liters and top it with 100%

amistre64 · Answer

lets check that :)

amistre64 · Answer

30(.2) + 10(1) = 40(.4)

6 + 10 = 16

16 = 16....we are goood

anonymous · Answer

OMG! i did that, but for some reason i thought it was wrong.... lame thanks dude!

amistre64 · Answer

:) youre welcome

preetha · Answer

good work Amistre64.  Nice set up of the equation.