Question

a caterer made an ice - cream punch by combining fruit juice that costs $5.00 per gallon with ice cream that costs $8.00 per gallon. how many gallons of each were used to make 50 gal of punch costing $5.60 per gallon? fruit juice gal ice cream gal

Explanation:

Step1: Set up variables

Let $x$ be the number of gallons of fruit - juice and $y$ be the number of gallons of ice - cream. We know two equations: $x + y=50$ (total volume equation) and $5x + 8y=5.6\times50$ (total cost equation).

Step2: Solve the first equation for $x$

From $x + y=50$, we get $x = 50 - y$.

Step3: Substitute $x$ into the second equation

Substitute $x = 50 - y$ into $5x + 8y=5.6\times50$. So $5(50 - y)+8y=280$.
Expand the left - hand side: $250-5y + 8y=280$.
Combine like terms: $3y=280 - 250$.
$3y=30$.

Step4: Solve for $y$

Divide both sides of $3y = 30$ by 3, we get $y = 10$.

Step5: Solve for $x$

Substitute $y = 10$ into $x=50 - y$, we get $x=50 - 10=40$.

Answer:

Fruit juice: 40 gal
Ice - cream: 10 gal