Question

In the following exercises, translate to a system of equations and solve.

Hannah has to make twenty five gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is \(1.79 per gallon and the cost of the fruit drink is \)2.49 per gallon. Hannah’s budget requires that the punch cost $2.21 per gallon. How many gallons of soda and how many gallons of fruit drink does she need

Short answer

The number of unit of soda is 10 gallons and number of unit of fruit drink is 15 gallons.

Step-by-step solution

Step 1. Given Information 

The given data is that Hannah has to make twenty five gallons of punch for a potluck. The punch is made of soda and fruit drink. The cost of the soda is $1.79 per gallon and the cost of the fruit drink is $2.49 per gallon. Hannah’s budget requires that the punch cost $2.21 per gallon.

Step 2. Explanation  

Let number of units of soda be x and number of units of fruit drink be y.

The punch cost is $$2.21$and total number of units are25 gallons

Thus, total value of punch is $25\times \$2.21=\$55.25$

Total value of punch can be expressed as $1.79x+2.49y=55.25--\left(1\right)$

Total units of punch can be expressed as$x+y=25--\left(2\right)$

Step 3. Calculation  

Multiply equation (2) with number $1.79$and write the revised equation.

$$\begin{gathered} 1.79(x+y)=1.79\left(25\right) \\ 1.79x+1.79y=44.75--\left(3\right) \end{gathered}$$

Solve the equation (3) and (1) by subtracting equation (3) from equation (1).

$$\begin{gathered} 1.79x+2.49y-1.79x-1.79y=55.25-44.75 \\ 0.7y=10.5 \\ y=15 \end{gathered}$$

Substitute the value of y in equation (2) to find the value of x.

$$\begin{gathered} x+y=25 \\ x+15=25 \\ x=10 \end{gathered}$$