A fruit punch that contains $70 \%$ fruit juice is combined with $100 \%$ fruit juice. How many ounces of each should be used to make 36 oz of a mixture that is $85 \%$ fruit juice?
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Part 1 of 2
Answer
To make \( 36 \) oz of a mixture that is \( 85\% \) fruit juice, we should use \( \boxed{18} \) ounces of \( 70\% \) fruit juice and \( \boxed{18} \) ounces of \( 100\% \) fruit juice
Step 1 ：Let \( x \) be the amount of \( 70\% \) fruit juice and \( y \) be the amount of \( 100\% \) fruit juice
Step 2 ：The total amount of the mixture is \( 36 \) oz, so we have the equation \( x + y = 36 \)
Step 3 ：The final mixture should be \( 85\% \) fruit juice, so we have the equation \( 0.7x + y = 0.85 \times 36 \)
Step 4 ：Solve the system of equations to find the values of \( x \) and \( y \)
Step 5 ：The solution is \( x = 18 \) and \( y = 18 \)
Step 6 ：To make \( 36 \) oz of a mixture that is \( 85\% \) fruit juice, we should use \( \boxed{18} \) ounces of \( 70\% \) fruit juice and \( \boxed{18} \) ounces of \( 100\% \) fruit juice
