Question

Yuri makes his own citrus vinaigrette salad dressing. He likes the dressing best if it contains 20% fruit juice. He has a bottle of dressing mixture that contains 50% juice and 3 cups of dressing that contains 10% juice. How much of the dressing mix with 50% juice should Yuri add to the dressing mix with 10% juice to get the dressing he prefers with 20% juice? Show your work.

Answer 1

lets call the number of cups of 50% juice added \(x\) and it will contain \(.5x\) cups of juice
at the moment he has 3 cups of 10% juice, so he has \(.3\) cups juice

Answer 2

when he adds the \(x\) cups of 50% juice, he will have \(3+x\) cups all together, and he wants that to be 20% juice, so set
\[.5x+.3=.2(x+3)\] and solve for \(x\)

Answer 3

probably easier to get rid of the annoying decimals and solve
\[5x+3=2(x+3)\]