Algebra 1b unit 4

Question

You are meeting with a group of students from your art class to work on a mural project. You each have an identical art kit but you arrange to share supplies. You bring ¼ of your kit, and your friend brings 2/3 of his. Together your kits are 2 pounds heavier than the third student’s kit, who brought 5/6 of hers. What is the weight of the complete kit? Write an equation that represents this problem. Include your solution and a check to make sure it’s accurate.

Answer 1

Let k be the weight of the art kits.

(1/4)k + (2/3)k = (5/6)k + 2

The least common denominator is 12 (4•3) = 12, (3•4) = 12, and (6•2) = 12 so we can use 12 as our denominator.

(1/4)(3/3)k + (2/3)(4/4)k = (5/6)(2/2)k + (2)(12/12)

Multiply each fraction by 1, i.e. 3/3 or 4/4, etc

(3/12)k + (8/12)k = (10/12)k + (24/12)

Combine the sides

(11/12)k = (10/12)k + (24/12)

Put all the k fractions to one side

(11/12)k - (10/12)k = (24/12)

Subtract

(1/12)k = (24/12)

Multiply each side by 12

k = 24

So the weight of each kit is 24 lbs.

Note: instead of multiplying each fraction by 1 (e.g. (1/4)(3/3)k) we could have just multiplied through both sides by the LCD, 12.

(12)[(1/4)k + (2/3)k] = (12)[(5/6)k + 2]

(12)(1/4)k + (12)(2/3)k = (12)(5/6)k + (12)(2)

3k + 8k = 10k + 24

3k + 8k - 10k = 24

11k - 10k = 24

k = 24