Question

Caleb cut a rope into 4 pieces. The lengths of the pieces of rope are 5 2/8 inches, 7 7/8 inches, 4 1/8 inches, and 3 3/8 inches. Which choice is the closest estimate of the length of the original rope? A. 1 foot 7 inches B 1 foot 9 inches C. 1 foot 11 inches D. 2 feet 2 inches

Answer 1

Step 1:

In this question, we are given the following:

Caleb cut a rope into 4 pieces.

The lengths of the pieces of rope are 5 2/8 inches, 7 7/8 inches, 4 1/8 inches, and 3 3/8 inches.

Which choice is the closest estimate of the length of the original rope?

A. 1 foot 7 inches B 1 foot 9 inches C. 1 foot 11 inches D. 2 feet 2 inches

Step 2:

The details of the solution are as follows:

We need to add up the individual pieces of rope:

`\begin{gathered} 5(2)/(8)\text{ inches + 7}(7)/(8)\text{ inches + 4}(1)/(8)\text{ inches + 3}(3)/(8)\text{ inches = 20}(5)/(8)\text{ inches} \\ \end{gathered}`

Next:

Converting

`20(5)/(8)\text{ inches to feet, we have that:}`
`\begin{gathered} 1\text{ inch = 0.0833333 foot} \\ 20(5)/(8)\text{ inches = 20}(5)/(8)\text{ x 0.0833333 = 1.718749313 foot \lparen1 feet 9 inches \rparen} \\ \approx\text{ 1 foot 9 inches \lparen OPTION B \rparen} \end{gathered}`

CONCLUSION:

The final answer is:

1 foot 7 inches ( OPTION B )