help with word problem!

Question

a cars radiator currently contains 2 quarts of liquid which is 25% antifreeze. How many quarts of 100% antifreeze must be added to increase the antifreeze content to 60%?

Answer 1

Brenda, the key is to recognize that you need to convert the percentages into amounts.

 

You start with 2 quarts of liquid that is 25% antifreeze, or you have 2 x .25 = .5 quarts of antifreeze to start with.

 

You are going to add another amount of liquid that is 100% antifreeze or you are going to add

L quarts of liquid and 1 x L quarts of antifreeze

 

When you are finished you are going to have L+2 quarts of liquid and L+.5 quarts of antifreeze, and

when we are finished we want the antifreeze content to be 60% or we want

 

L+2 quarts of liquid that is 60% antifreeze or L+.5 quarts of antifreeze, so

.6(L+2)=L+.5

.6L + 1.2 = L+.5

-.6L - .5 = -.6L -.5

0.7=.4L

.7/.4=.4L/.4

L= 1.75 quarts of Antifreeze.

 

Check

1.75+.5 quarts of antifreeze=2.25

2+1.75 quarts of fluid = 3.75

2.25/3.75=.6=60%

 

I hope this helps.  John