Solution Problem

[YummyNoodles]

Original Problem: A car radiator is filled with 5L of a 25% antifreeze solution. How many liters must be drawn off and replaced by a 75% antifreeze solution to leave the radiator filled with a 55% antifreeze solution?

I was a little confused by the wording of this problem so I need some help with setting up the equation. I interpreted it as the amount drawn is off the same as the amount of new solution added so I set c = L of solution drawn off & replaced, and set up the equation as 0.25(5) - c + 0.75(c) = 0.55(5) but ended up with a negative solution. Any tips on how to begin/set up would be appreciated.

 

[Deleted member 4993]

Original Problem: A car radiator is filled with 5L of a 25% antifreeze solution. How many liters must be drawn off and replaced by a 75% antifreeze solution to leave the radiator filled with a 55% antifreeze solution?

I was a little confused by the wording of this problem so I need some help with setting up the equation. I interpreted it as the amount drawn is off the same as the amount of new solution added so I set c = L of solution drawn off & replaced, and set up the equation as 0.25(5) - c + 0.75(c) = 0.55(5) but ended up with a negative solution. Any tips on how to begin/set up would be appreciated.

Your equation should be derived as follows:

After you take out 'c' litres of old (25%) antifreeze out.

We have (5-c)0.25 anti-freeze now

We add (c)(0.75) L of antifreeze.

Amount of antifreeze in new solution 5 * 0.55 L.

Now, mass balance (or volume balance with no change in density) of anti-freeze gives us:

(5-c)0.25 + c*0.75 = 5 * 0.55

0.5*c = 5*0.30 ........................................[edited]

No negative 'c'.

 

[JeffM]

The clue here I think is the use of the word "filled" twice. So it makes sense to assume that the volume of 25% solution removed and the volume of 75% solution added are the same. Good work.

Your equation is almost right. After you take c of the 25% solution out, what is the percentage of the remainder? Obviously still 25%. So we are mixing 5 - c at 25% and c at 75% to get 5 at 55%. The equation almost writes itself.

[MATH]0.25(5 - c) + 0.75c = 0.55 * 5 \implies 25(5 - c) + 75c = 275 \implies \text {WHAT?} [/MATH]

 

[YummyNoodles]

Thanks so much for your help!