Question

you have two saltwater solutions.one consists of 20% salt, and the other consists of 15% salt.

if you wanted to make 5 gallons of a 19% solution, what volume of each solution should you add?

Answer 1

lets put \(x\) as the number of gallons of 20% solution, which makes the number of gallons of 15% solution \(5-x\) since the total is 5 gallons

Answer 2

then you know that the \(x\) gallons of 20% solution will have \(.20x\) salt, and the \(5-x\) gallons of 15% solution will have a total of \(.15(5-x)\) salt
therefore the total amount of salt will be
\[.2x+.15(5-x)\]and since you want this total to be 19% of 5, which is \(.95\) set
\[.2x+.15(5-x)=.95\] and solve for \(x\)

Answer 3

easier to solve if you clear the decimal by multiplying both sides by 100 to get
\[20x+15(5-x)=95\] and solve that one

Answer 4

you good from there?

Answer 5

i think so

Answer 6

ok, don't forget at the end that you need both \(x\) the number of gallons of 20% solution, and also \(5-x\) the number of gallons of 15% solution

Answer 7

i got x=4.so 80 gallons of 20% and 1 gallon of 15% right?

Answer 8

yeah \(x=4\) so 4 gallons of 20% solution and 1 gallon of 15%
not sure why you wrote 80 though

Answer 9

okay thanks so much!

Answer 10

yw