SOLUTION: Janelle cut a board 30 feet long into 2 pieces. The ratio of the lengths of the 2 pieces is 2:3. What is the length, to the nearest foot, of the shorter piece? a) 5 b) 6 c)

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Question 256003: Janelle cut a board 30 feet long into 2 pieces. The ratio of the lengths of the 2 pieces is 2:3. What is the length, to the nearest foot, of the shorter piece?
a) 5 b) 6 c) 12 d) 15 e) 18
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let s = shorter board.

let m = longer board.

equation of ratio of shorter board to longer board is:

s/m = 2/3

multiply both sides of this equation by m to get:

s = (2*m)/3

total length of the 2 pieces is 30 feet.

equation for that is:

s + m = 30

substitute 2*m/3 for s to get:

2*m/3 + m = 30

multiply both sides of this equation by 3 to get

2*m + 3*m = 90

combine like terms to get:

5*m = 90

divide both sides of this equation by 5 to get:

m = 90/5 = 18

m is the longer board.

s is the shorter board.

s = 2*m/3 = 2*18/3 = 2*6 = 12

shorter board is 12 feet long
longer board is 18 feet long.

12 + 18 = 30 (sum is good)

12/18 = 6/9 = 2/3 (ratio is good)

easier way to solve this is:

ratio of shorter board to larger board is 2:3

that means that the shorter board has 2 parts and the longer board has 3 parts.

2 parts + 3 parts = 5 parts that make up the total board.

there are 30 feet / 5 parts = 6 feet of length to each part.

the shorter board = 2 parts = 2 * 6 = 12 feet in length.

the longer board = 3 parts = 3 * 6 = 18 feet in length.