Question

A pipe is at least 21 feet long, and you want to cut it into three pieces. the second piece is to be twice as long as the first piece, and the third piece is to be 1 foot longer than the second piece. what is the minimum length of the first piece?

Answer 1

The minimum length of the first piece is 4 feet.

Explanation

Suppose, the length of the first piece is $x$ feet.

The second piece is twice as long as the first piece. So, the length of the second piece $= 2x$ feet.

Now the third piece is 1 foot longer than the second piece. So, the length of the third piece $=(2x+1)$ feet.

Given that, the total length of the pipe is at least 21 feet. So, the inequality will be .....

$x+(2x)+(2x+1)\geq 21 \\ \\ 5x+1 \geq 21\\ \\ 5x\geq 20\\ \\ x\geq \frac{20}{5} \\ \\ x\geq 4$

Thus, the minimum length of the first piece is 4 feet.