what is the equation?

Question

The railings for the deck in Example 4 have three different lengths of board. The shortest is 10 inches less than the next shortest, which is 14 inches shorter than the longest. Their combined length is supposed to match the overall length of the deck, which in this case is 20 feet. How long should each piece be?

Answer 1

Let x = the shortest length

Let x + 10 = the middle length

Let x + 24 = the longest length

20 feet = 20(12) = 240 inches

x + x + 10 + x + 24 = 240

3x + 34 = 240

3x = 206

x = 68.66666 inches ≈ 5.7 feet 

x + 10 = 78.66666 ≈ 6.6 feet

x + 24 = 92.66666 ≈ 7.7 feet