solution type problems

[kapitalist]

I get hung up on these "solution" problems.

Question: How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution.

Can you please tell me how to set these "solution" problems up...as I get stuck on all the types.

not sure how to use the "spoiler" button so the answer is .50 gallons

[Vemuri]

I get hung up on these "solution" problems.

Question: How many gallons of water must be mixed with 1 gallon of a 15% salt solution to obtain a 10% salt solution.

Can you please tell me how to set these "solution" problems up...as I get stuck on all the types.

not sure how to use the "spoiler" button so the answer is .50 gallons

I agree kapitalist, solution problems can sometimes get very tricky, especially when you are running against time.

For the problem you stated, I think the best way to approach it is to be logical. If 1 gallon of solution contains 15% of salt (15 parts of salt & 85 parts of water), then by adding 1 gallon of water (100 parts of water) will make the salt percentage drop by half (i.e 15/200 = 7.5%). So, half gallon of water should be enough to obtain 10% salt solution.

Below is an attempted graphical representation. Hope it helps

[kapitalist]

Your picture helped and I get the problem, but is there some way to always setup these solution type problems??

[scoobydooby]

1g of 15% salt solution has 0.15g of salt and the rest water.

let w gallons of water be added to this solution, the amount of salt remains the same. the new solution has 10% salt concentration

or 0.15g/(1g+w)=10/100
or 10w=15-10
or w=0.5g