Question

Write an equation to solve each problem and then solve it. b A 25-foot long board is to be cut into two parts. The longer part is one foot more than twice the shorter part. How long is each part?

Answer 1

8 and 17

Explanation:

Let's say the smaller number is x. The question says "The longer part is one foot more than twice the shorter part" so we reverse that using x which becomes x+2x+1=25 and x=8 so 8+8*2+1=25 => 8+17=25 so the answer is 8 and 17, please like and 5 star rate

Answer 2

• shorter part: 12 ft
• longer part: 13 ft

Explanation:

Let s represent the length of the shorter part (in feet). Then the longer part has length (s+1), and the total length of the two parts is ...

s + (s+1) = 25

2s = 24 . . . . . . . subtract 1, simplify

s = 12 . . . . . . . . . divide by 2; the length of the shorter part

s+1 = 13 . . . . . . . the length of the longer part

The shorter part is 12 feet long; the longer part is 13 feet long.

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Comment on this problem type

You will note that the smaller number is half the difference of the total length (25) and the difference in lengths (1). This is the generic solution to a "sum and difference" problem. The smaller number is half the difference of the given numbers, and the larger number is half their sum: (25+1)/2 = 13.