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 30 granola bars. The camp bought a total of 6 boxes that have 100 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.​

Answer 1

The system of equations is

`\begin{cases}\text{x}+\text{y} = 6\\10\text{x}+30\text{y} = 100\\\end{cases}`

x is the number of small boxes

y is the number of large boxes

That system solves to (x,y) = (4,2)

In other words, x = 4 and y = 2

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Work Shown:

x = number of small boxes

y = number of large boxes

x+y = 6 total boxes

y = 6-x after subtracting x from both sides

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10x = number of bars from the small boxes only

30y = number of bars from the large boxes only

10x+30y = total number of bars

10x+30y = 100

10x+30(6-x) = 100

10x+180-30x = 100

-20x = 100-180

-20x = -80

x = -80/(-20)

x = 4 small boxes were purchased

y = 6-x = 6-4 = 2 large boxes were purchased

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Check:

If you bought x = 4 small boxes, then that gives 10x = 10*4 = 40 granola bars so far. Then y = 2 large boxes gives another 30y = 30*2 = 60 granola bars. That's 40+60 = 100 total, which confirms the answers.