https://file.aiquickdraw.com/mathbot/file/1726586429880ld9rp0oj.jpg

We are tasked with formulating a system of equations based on the problem provided.

### Information from the problem:
- A food truck sells:
  - Hot dogs at $6 each.
  - Popsicles at $8 each.
  - Hamburgers at $11 each.
- The food truck made a total of 174 sales and $1488 in revenue.
- They sold twice as many hamburgers as popsicles.

### Variables:
- Let $ x $ be the number of hot dogs sold.
- Let $ y $ be the number of popsicles sold.
- Let $ z $ be the number of hamburgers sold.

### System of Equations:
1. The total number of items sold is 174:
   \[
   x + y + z = 174
   \]
2. The total revenue from sales is $1488:
   \[
   6x + 8y + 11z = 1488
   \]
3. The number of hamburgers sold is twice the number of popsicles sold:
   \[
   z = 2y
   \]

Thus, the system of equations is:
\[
\begin{aligned}
1. & \quad x + y + z = 174 \\
2. & \quad 6x + 8y + 11z = 1488 \\
3. & \quad z = 2y
\end{aligned}
\]

Would you like a breakdown of how these equations were derived or further assistance? Here are some related questions for practice:

1. How would the system change if hamburgers were sold at $12 instead of $11?
2. What would the system of equations look like if there were 200 total sales instead of 174?
3. How would you solve the system of equations algebraically?
4. What happens to the system if the price of popsicles decreases to $7?
5. How could you use substitution or elimination to simplify the system?

**Tip**: When creating systems of equations, always ensure that each equation represents a distinct piece of information (e.g., total sales, total revenue, and relationships between variables).

A food truck sells three types of food: a hot dog for $6, a popsicle for $8, and a hamburger for $11. Yesterday, the food truck made a total of 174 sales for a total of $1488. They sold twice as many hamburgers as popsicles. Write the equations to find the number of each type of popsicles, hot dogs, and hamburgers sold. Let x be the number of hot dogs sold, y be the number of popsicles sold, and z be the number of hamburgers sold. Do not solve.

Learn how to set up a system of equations to solve a food truck sales problem. In this scenario, a food truck sold hot dogs, popsicles, and hamburgers with different prices. This problem covers setting up linear equations based on total sales and revenue, perfect for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation