Question

A 10% salt solution is to be mixed with a 20% salt solution to obtain 15 gallons of a 12% salt solution. how many gallons of each should be used?

Answer 1

the trick with these problems is to keep track of the amount of "stuff" and the amount of liquid separately. a 10% solution has 0.1 units of salt in 1 unit of solution. if we are trying to make 15 gallons of 12% salt solution, there will be 15*0.12 = 1.8 units of salt in the 15 gallons.

Answer 2

so we have two equations to write:

let's call x the amount of 10% salt solution
let's call y the amount of 20% salt solution

x+y = 15 — we are making 15 gallons of 12% solution
0.1x + 0.2y = 15*0.12 — the amount of salt in the 10% solution + the amount of salt in the 20% solution = the amount of salt in 15 gallons of 12% solution

Answer 3

it's really a coin problem in disguise :-)

Answer 4

kay let me try and solve it :)

Answer 5

yeah it seems almost exactly the same

Answer 6

what do you get for your result?

Answer 7

y=3? x=12?

Answer 8

12+3=15

Answer 9

excellent! you can check your answer:

12 gallons of 10% = 1.2 units of salt
3 gallons of 20% = 0.6 units of salt
total 1.8 units of salt

15 gallons of 12% = 15*0.12 = 1.8 units of salt

12+3 = 15

everything checks out!

just be sure to label the answer so there's no question about whether x is the 10% or the 20%

Answer 10

heartbreaking to do the problem right and then get dinged for something stupid like switching the numbers when writing out the answer! :-)

Answer 11

and i forgot my units, dang. thanks :)