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A 72 foot pipe is cut into three sections. The longest section is five times as long as the shortest, and the middle-sized section is 9 feet longer than the shortest. Complete the diagram by giving a and b as expressions involving x. Do not solve the problem.

User Adnan Ali
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Answer:

Explanation:

Let x be the length of the shortest section of the pipe.

Then, according to the problem:

The longest section is 5 times as long as the shortest, so its length is 5x.

The middle-sized section is 9 feet longer than the shortest, so its length is x + 9.

The sum of the lengths of the three sections must equal the length of the original 72-foot pipe:

x + 5x + (x + 9) = 72

Simplifying the left-hand side, we get:

7x + 9 = 72

Subtracting 9 from both sides, we get:

7x = 63

Dividing by 7, we get:

x = 9

Therefore:

The length of the shortest section is x = 9 feet.

The length of the longest section is 5x = 45 feet.

The length of the middle-sized section is x + 9 = 18 feet.

To complete the diagram, we can label the sections as follows:

Shortest section: |---a---|

Middle-sized section: |-----b-----|

Longest section: |----------5a----------|

where a = 9 and b = a + 9. Therefore:

a = 9 feet

b = a + 9 = 18 feet

User Tikhop
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