Question

Sara is mixing together a fruit punch for a party. She's made 4 gallons of punch with a mixture of 50% juice. Her mother tells her to change it to a mixture of 60% juice. How much fruit juice should be added to make the mixture 60% fruit juice

Answer 1

$\bf \begin{array}{lccclll} &amount(gallons)&juice&\textit{juice amount}\\ &--------&-----&-----\\ \textit{50\% punch}&4&0.50&(4)(0.50)\\ \textit{pure juice}&x&1.00&(x)(1.00)\\ -----&-----&-----&-----\\ mixture&4+x&0.60&(4+x)(0.60) \end{array}$

notice, that, pure juice is 100% juice, dohhh, thus 100/100 = 1.00
50% is 50/100 or 0.50 in decimal format

so..... whatever those two quantities amount to, that is, the 50% and pure juice, or (4)(0.50) + (x)(1.00)
they will equal the mixture desired 60% juice, or 0.60, namely (4+x)(0.60)

thus    (4)(0.50) + (x)(1.00) = (4+x)(0.60)

solve for "x"