Question

A radiator contains 15 quarts of fluid, 30% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 35% antifreeze? (Round your answer to two decimal places.)

Answer 1

\[\%Antifreeze = \frac{V_{Antifreeze}}{V_{Fluid}}\]
\[V_{Fluid}=\frac{V_{Antifreeze}}{\%Antifreeze}\]
\[V_{Antifreeze}=V_{fluid} * \%Antifreeze\]
I want to find the amount of antifreeze in a 15 quart solution with 30% antifreeze
\[V_{Antifreeze}=15*0.30\] =18/4 quarts of antifreeze
Similarly, I want to find the amount of antifreeze in a 15 quart solution with 35% antifreeze first.
\[V_{Antifreeze}=15*0.35\] = 21/4 quarts of antifreeze

Answer 2

the difference between 21/4 and 18/4 is 3/4 quarts, which is the amount of pure antifreeze I've added in.

Answer 3

SO the V_fluid I replaced with 3/4 quarts of antifreeze is (3/4)/ 0.35

Answer 4

Therefore, I must replace 15/7 quarts of the fluid with pure antifreeze :-D

Answer 5

But I'm mistaken

Answer 6

It's telling me that I have the wrong answer.

Answer 7

:(

Answer 8

I think I figured it out now:

\[\text{Antifreeze}\ \ \ \%100\ \ \ x\text{ quarts}\]
\[\text{Fluid }\%30\ \ \ (15-x)\text{quarts}\]
\[\text{New mixture}\ \ \ \ \%35\ \ \ \ 15quarts\]

Answer 9

\[100x + 30(15-x)=35*15\]
solve for x
\[x = \frac{15}{14}\text{quarts}\]

Answer 10

THANKS!

Answer 11

therefore, 1.07 quarts of fluid must be drained and replaced with pure antifreeze

Answer 12

Yeah, Thanks!

Answer 13

Can you help me with my other word problem too?

Answer 14

The one about investing.