Question 264815
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.