SOLUTION: If a walkway can be made from either 18 ft long boards or 14 ft long boards without anyone needing to be cut, then what is the shortest possible length of the walkway? How long

Question 264815: If a walkway can be made from either 18 ft long boards or 14 ft long boards without anyone needing to be cut, then what is the shortest possible length of the walkway?
How long is the walkway if you know that 16 fewer boards are needed if the 18 ft long boards are used?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
shortest length of the walkway would have to be 14 feet with the use of 1 board since they didn't tell you how many boards were required nor how long the walkway had to be.

if you know that use of the 18 foot boards requires 16 less boards in total then your formula would be:

x = number of 18 foot boards.
y = number of 14 foot boards.

x = y - 16

total length is x * 18 and y * 14.

since they both equal total length then they both equal to each other, so you get:

x * 18 = y * 14.

you know that x = y - 16, so substitute in this equation to get:

(y-16)*18 = y*14

simplify to get:

18*y - 16*18 = 14*y

subtract 14*y from both sides of this equation and add 16*18 to both sides of this equation to get:

18*y - 14*y = 16*18

simplify and combine like terms to get:

4*y = 288

divide both sides of this equation by 4 to ge:

y = 288/4 = 72

you need 72 * 14 foot boards

you need 72-16 = 56 * 18 foot boards.

72*14 = 1008

56*18 = 1008

the question was:

how long is the walkway.

the answer is:

the walkway is 1008 feet long.

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