Question: User: Name Jaki Rodriguez Date 04/15/26 Period 7th
Classwork - Applications of Linear Relationships
1. A coffee truck owner sells three sizes of iced coffee. The small sells for $5.50$, the medium sells for $6.75$, and the large is $7.50$. Last Saturday, the vendor sold $95$ items for a total of $628$. The vendor sold $13$ more items for $6.75$ than for $7.50$. Write a system of equations you could use to determine how many iced coffees were sold. Define the variables.
1. **Problem:** A coffee truck owner sells small, medium, and large iced coffees at prices $5.50$, $6.75$, and $7.50$ respectively. They sold $95$ items totaling $628$. The number of medium coffees sold is $13$ more than the number of large coffees sold. Find the system of equations to determine how many of each size were sold.
2. **Define variables:**
- Let $x$ = number of small coffees sold
- Let $y$ = number of medium coffees sold
- Let $z$ = number of large coffees sold
3. **Write equations:**
- Total items sold: $$x + y + z = 95$$
- Total sales amount: $$5.50x + 6.75y + 7.50z = 628$$
- Medium coffees sold is 13 more than large: $$y = z + 13$$
4. **System of equations:**
$$\begin{cases}
x + y + z = 95 \\
5.50x + 6.75y + 7.50z = 628 \\
y = z + 13
\end{cases}$$
This system can be solved to find $x$, $y$, and $z$.
**Final answer:** The system of equations is:
$$\begin{cases}
x + y + z = 95 \\
5.50x + 6.75y + 7.50z = 628 \\
y = z + 13
\end{cases}$$