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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 8 granola bars and each large box has 12 granola bars. The camp bought a total of 14 boxes that have 148 granola bars altogether. Determine the number of small boxes purchased and the number of large boxes purchased.

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absor201

5 small boxes and 9 large boxes were purchased.

Step-by-step explanation:

Given,

Granola bars in small box = 8

Granola bars in large box = 12

Total boxes bought = 14

Total bars = 148

Let,

Number of small boxes = x

Number of large boxes = y

According to given statement;

x+y=14    Eqn 1

8x+12y=148    Eqn 2

Multiplying Eqn 1 by 8

[tex]8(x+y=12)\\8x+8y=112\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](8x+12y)-(8x+8y)=148-112\\8x+12y-8x-8y=36\\4y=36[/tex]

Dividing both sides by 4

[tex]\frac{4y}{4}=\frac{36}{4}\\y=9[/tex]

Putting y = 9 in Eqn 1

[tex]x+9=14\\x=14-9\\x=5[/tex]

5 small boxes and 9 large boxes were purchased.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/11343416
  • brainly.com/question/11416224

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