Question

Sami cut 6 and three-fourths inches off a long roll of paper. If the roll is now 36 and one-third inches long, how long was the original roll of paper? Write an equation and solve it to find the answer.

29 and StartFraction 7 Over 12 EndFraction inches
30 and StartFraction 7 Over 12 EndFraction inches
42 and StartFraction 1 Over 12 EndFraction inches
43 and StartFraction 1 Over 12 EndFraction inches

Answer 1

To find the original length of the roll of paper, we'll set up an equation based on the information given in the problem.

Let \( x \) represent the original length of the roll of paper. According to the information provided:

1. Sami cut \( 6 \frac{3}{4} \) inches off the roll.
2. After this cut, the roll is \( 36 \frac{1}{3} \) inches long.

We can express this situation as the equation:

\[
x - 6 \frac{3}{4} = 36 \frac{1}{3}
\]

Now, let's convert the mixed numbers into improper fractions to make calculations easier.

1. For \( 6 \frac{3}{4} \):
\[
6 \frac{3}{4} = 6 \times 4 + 3 = 24 + 3 = 27 \quad ≈ \frac{27}{4}
\]

2. For \( 36 \frac{1}{3} \):
\[
36 \frac{1}{3} = 36 \times 3 + 1 = 108 + 1 = 109 \quad ≈ \frac{109}{3}
\]

Now, substitute these into the equation:

\[
x - \frac{27}{4} = \frac{109}{3}
\]

To solve for \( x \), we add \( \frac{27}{4} \) to both sides of the equation:

\[
x = \frac{109}{3} + \frac{27}{4}
\]

To add these two fractions, we first need a common denominator. The least common multiple of 3 and 4 is 12. We can rewrite each fraction as follows:

1. Convert \( \frac{109}{3} \):
\[
\frac{109}{3} = \frac{109 \times 4}{3 \times 4} = \frac{436}{12}
\]

2. Convert \( \frac{27}{4} \):
\[
\frac{27}{4} = \frac{27 \times 3}{4 \times 3} = \frac{81}{12}
\]

Now we can add:

\[
x = \frac{436}{12} + \frac{81}{12} = \frac{436 + 81}{12} = \frac{517}{12}
\]

Now, we can simplify this fraction if necessary:

\[
\frac{517}{12} = 43 \frac{1}{12} \quad \text{(since 517 ÷ 12 = 43 remainder 1)}
\]

Thus, the length of the original roll of paper was:

\[
\boxed{43 \frac{1}{12}} \text{ inches}
\]