Question

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 10 granola bars and each large box has 24 granola bars. the camp bought a total of 10 boxes that have 184 number of large boxes purchased. define the variables that you use to write the system. let = let = system of equations:

Explanation:

Step1: Define variables

Let \( x \) be the number of small boxes and \( y \) be the number of large boxes.

Step2: First equation (total number of boxes)

The total number of boxes is 10, so \( x + y = 10 \).

Step3: Second equation (total number of granola bars)

Each small box has 10 bars, each large box has 24 bars, and total bars are 184. So \( 10x + 24y = 184 \).

System of Equations:

\( x + y = 10 \)

\( 10x + 24y = 184 \)

(Note: If we were to solve this system, we could use substitution or elimination. For example, from the first equation \( x = 10 - y \), substitute into the second equation: \( 10(10 - y) + 24y = 184 \), \( 100 - 10y + 24y = 184 \), \( 14y = 84 \), \( y = 6 \), then \( x = 10 - 6 = 4 \). But the question only asked for the system of equations and defining variables.)

Answer:

Let \( x \) = number of small boxes, \( y \) = number of large boxes.

System of Equations:

\( x + y = 10 \)

\( 10x + 24y = 184 \)