A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 12 granola bars and each... A summer camp is organizing a hike and needs to buy granola bars for the campers. The granola bars come in small boxes and large boxes. Each small box has 12 granola bars and each large box has 18 granola bars. The camp bought a total of 15 boxes that have 240 granola bars altogether. Write a system of equations that could be used to determine the number of small boxes purchased and the number of large boxes purchased. Define the variables that you use to write the system.
Understand the Problem
The question is asking us to formulate a system of equations based on the number of granola bars in small and large boxes purchased by a camp. We are to define the variables representing the number of small and large boxes to write this system.
Answer
The system of equations is: \[ \begin{align*} 1. & \quad x + y = 15 \\ 2. & \quad 12x + 18y = 240 \end{align*} \]
Answer for screen readers
The system of equations is:
[
\begin{align*}
- & \quad x + y = 15 \
- & \quad 12x + 18y = 240 \end{align*} ]
Steps to Solve
-
Define the Variables
Let ( x ) represent the number of small boxes purchased, and ( y ) represent the number of large boxes purchased. -
Formulate the Total Boxes Equation
The problem states that the total number of boxes purchased is 15. This can be expressed as:
$$ x + y = 15 $$ -
Formulate the Total Granola Bars Equation
Each small box contains 12 granola bars and each large box contains 18 granola bars. The total number of granola bars is 240. This can be expressed as:
$$ 12x + 18y = 240 $$ -
Final System of Equations
The system of equations can therefore be written as:
[ \begin{align*} -
& \quad x + y = 15 \
-
& \quad 12x + 18y = 240 \end{align*} ]
The system of equations is:
[
\begin{align*}
- & \quad x + y = 15 \
- & \quad 12x + 18y = 240 \end{align*} ]
More Information
This system of equations will help determine how many small and large boxes were purchased based on the total boxes and granola bars.
Tips
- Not defining the variables correctly: Ensure to clearly designate one variable for each type of box.
- Ignoring units in equations: Always include the quantities (boxes, granola bars) in the formulation of your equations.
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