Can someone please help me with this math word problem?

Question

"A car radiator contains 10 liters of a 30% antifreeze solution. How many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?"

I am completely lost on this one, and any help would be appreciated. If you can only give me the formulas/equations, that would be great too (: Thanks!

Answer 1

First, remember that, when you take out some of the solution, you are removing some of the antifreeze, so it's not a case of removing 2 litres and adding 2 litres of antifreeze.

Ok, now the solution

To get 50% antifreeze, you obviously need 50% of the radiator to be non-antifreeze. At the moment, it is 70% non-antifreeze, so we need to remove 20% of the total radiator volume of pure non-antifreeze, or 2 litres.

Therefore 2 litres is 70% of the total volume of the mixed solution we need to remove (since, as I said before, you can't just remove the non-antifreeze from a mixed solution, and the solution is 70% non-antifreeze). 2 *100/70 = 2.86L. We need to remove about 2.86L of the solution.
-----------------
Start with 10L (3L antifreeze / 7L non-antifreeze)
Remove 2.86L (0.86L antifreeze / 2L non-antifreeze)
Leaves 7.14L (2.14L antifreeze / 5L non-antifreeze)
Top up with 2.86L antifreeze
Result: 10L (5L antifreeze / 5L non-antifreeze)

Answer 2

total volume of the solution = 10 liters
volume of antifreeze solution in it = 30% of total volume = (30/100)*10 = 300/100 = 3 liters
therefore, if the resulting solution is to be 50% antifreeze = (50/100)*10 = 500/100 = 5 liters
then add 5-3 = 2 liters of antifreeze

:-):-)

Answer 3

IT'S NOT 2 LITERS. ASSUME YOU HAVE 100ML JACK DANIELS AND 100ML COLA IN A GLASS. CAN YOU TAKE ONLY COLA AWAY AND REPLACE IT WITH 100ML JACK SO THAT YOU GET 100% JACK IN THE GLASS? OBVIOUSLY NOT, THINK ABOUT IT

Assume that you replace X liters with pure antifreeze.

(10 - X) liters of 30% antifreeze left and X liters of pure antifreeze are added.

The total amount of antifreeze would be (10 - X) * 0.3 + X

Since it should be 50% antifreeze of 10 liters, the amount of antifreeze after this operation should be equal to 10*0.5 = 5 liters.

Hence, we get the equation:
(10 - X) * 0.3 + X = 5
0.7X = 2
X = 20 / 7, which is about 2.857 liters

Answer 4

if it has 10 liters at 30% that means 3 liters are pure and 7 liters are water. that means you would have to replace 2 liters with pure antifreeze to get a 50% solution

Answer 5

The answer is 16.67 litres.

Okay, if 10 litres = 30% antifreeze then 5 litres must = 15%.

which also means that 1.67 litres = 5%

because 5 divided by 3 = 1.67.

and because 30 + 20 = 50 you need to add 20% on which you would have noticed is the 5 litres + 1.67 litres (because the percentage = 15 + 5 = 20%)

5 + 1.67 = 6.67% then add the 10% and you get 16.67%

Answer 6

this is horrible simple..
30% from 10 is 3 liters.
to have 50% from 10 .. that means 5 liters
so you have to replace 2 liters . 5-3=2.
very very easy !

Answer 7

Peanut