Question

1) Three gallons of a mixture is 60% water by volume. Determine the number of gallons of water that must be added to bring the mixture to 75% water.
2) A car radiator contains 10 quarts of a 30% antifreeze solution. How many quarts will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?

Answer 1

60% = 0.6
A 60% mixture of water means that the ratio of water content to the total volume is:

\(\dfrac{water~content}{total ~volume} = 0.6\)

If there are 3 gallons of the mixture, then how much water is there in the mixture?

Answer 2

you can use the ratio
$$ \large \frac{3 \times 0.60 + x }{3 + x } =0 .75 $$

Answer 3

where x = gallons of water added

Answer 4

Is there a formula that can relate to systems of equations?

Answer 5

Keeping track of units to muscle though it.

Answer 6

ratio of gal H2O / gal Solution

Answer 7

Now - 0.6*3 gal H20, and , 3 gal Solution
change - x gal H2O, and x gal solution
End - want 0.75 gal H2O / 1 gal Solution to , (75%)

Answer 8

I don't understand.

Answer 9

This is what you have to start, amt of water/amt of solution
\[\Large \frac{ (3*0.6 )~gal~H2O }{ (3)~gal ~Soln } = \frac{ 0.6 ~gal~H2O }{ 1~gal~Soln }\]

Then you want to add X water, to bring it up to 0.75 gal H2O/1 gal Soln
\[\frac{ (3*0.6 + X)~gal~H2O }{ (3 + X)~gal ~Soln } =\frac{ 0.75 ~gal~H2O }{ 1 ~gal~Soln }\]

Answer 10

notice the increase in water X , also increases the solution volume the same amount.

Solve for X gal H2O to add

Answer 11

Why would you use 1 gallon?

Answer 12

to make it easy to see the percent water, 0.75 / 1 = 75/100 = 75%, you want your ratio to be that

Answer 13

There probably is a formula that looks like this in the book, but this is what i came up with from using the units.

Answer 14

solving this for the X gal H2O

\[\frac{ (3*0.6 + X)~gal~H2O }{ (3 + X)~gal ~Soln } =\frac{ 0.75 ~gal~H2O }{ 1 ~gal~Soln }\]

\[\large x = 1.8 ~gal ~H2O\]

If you started with (3*0.6) = 1.8 gallons of water per 3 gallons of solution, you have a 60% mixture.
If you then add an additional x=1.8 gallons of water, you will now have

(1.8+1.8) = 3.6 gallons of water, and (3+1.8)=4.8 gallons of total solutipon
3.6 gal water / 4.8 gal of total solution, equals 75% water mixture, so that is correct

Answer 15

I think this is the [C1]*V1 = [C2]* V2 , dilution formula application from chem 1 maybe

Answer 16

\[\frac{ (3*0.6+x) }{ (3+x) } = \frac{ 0.75 }{ 1 }\]


\[\frac{ 1.8+x }{ 3+x } = \frac{ 0.75 }{ 1 }\]

Answer 17

Right? Or would you not simplify?

Answer 18

I don't really understand why x is 1.8 gallons.

Answer 19

solve that, cross multiply

1*(1.8+x) = 0.75*(3+x)
1.8 + x = 0.75*3 + 0.75*x