SOLUTION: Lolo Jose constructs a wooden ladder with 6 steps. The height of the ladder is 6ft longer than the lengths of the steps. What are the dimensions of the ladder if only 20 feet of wo

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Question 1167529: Lolo Jose constructs a wooden ladder with 6 steps. The height of the ladder is 6ft longer than the lengths of the steps. What are the dimensions of the ladder if only 20 feet of wood is used?
Answer by Theo(13342) About Me  (Show Source):
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let H = the height of the ladder.
let S = the length of each step.

the height of the ladder is 6 feet longer than the length of each step.

equation for that is H = S + 6

the ladder has 2 pieces of wood that are as long as the height of the ladder and 6 pieces of wood that are as long as the length of each step.

the total amount of wood is 20 feet.

therefore:

2H + 6S = 20

since H = S + 6, then:

2 * (S + 6) + 6S = 20

simplify to get 2S + 12 + 6S = 20

combine like terms to get 8S + 12 = 20

subtract 12 from both sides of the equation to get 8S = 8

solve for S to get S = 1

the length of each step is equal to 1 foot.

the height of the ladder is S + 6 = 7 feet.

there are 2 pieces of wood that are 7 feet long each and 6 pieces of wood that are 1 foot long each.

total amount of wood = 2 * 7 + 6 * 1 = 14 + 6 = 20.

the dimensions of the ladder are 7 feet high by 1 foot wide.