Chapter 9, Problem 34CR

To determine

To write a system of equations and solve the system to find the numbers.

Answer to Problem 34CR

The system of equations can be written as:

  $\begin{array}{l}\text{2x}+\text{y}=24\\ \text{x}=\frac{1}{2}\text{y}\end{array}$

The solution of the system of equations is $\left(6,12\right)$ .

The solution means the café sold $\text{12}$ strawberry smoothies and $\text{6}$ vanilla smoothies.

Explanation of Solution

Given information:

The given statement is:

“A café sells strawberry smoothies and vanilla smoothies. On Monday, the café sold twice as many strawberry smoothies as vanilla smoothies. The total number of smoothies sold was $24$ . Write a system of equations to represent this situation. Then solve the system and explain what the solution means.”

Calculation :

The system of equations can be written as:

  $\begin{array}{l}\text{2x}+\text{y}=24\\ \text{x}=\frac{1}{2}\text{y}\end{array}$

The graph of the equations are:

The graph is intersecting at $\left(6,12\right)$ .

Check by substituting the values of $\text{x and y}$ by $\left(6,12\right)$ :

  $\begin{array}{l}\text{2x}+\text{y}=24\\ 2\left(6\right)+12=24\\ 12+12=24\\ 24=24\\ \\ \text{x}=\frac{1}{2}\text{y}\\ 6=\frac{1}{2}\left(12\right)\\ 6=6\end{array}$

Hence, the solution of the system of equations is $\left(6,12\right)$ .

The solution means the café sold $\text{12}$ strawberry smoothies and $\text{6}$ vanilla smoothies.