Nadia takes a ribbon that is 48 inches long and cuts it in two pieces. One piece is three times as long as the other. How long is each piece?

To find the lengths of the two pieces of ribbon, let's denote the length of the shorter piece as \( x \) inches. The longer piece, being three times as long as the shorter one, will then be \( 3x \) inches.

The total length of the ribbon is given as 48 inches. Therefore, we can write the equation:

\[ x + 3x = 48 \]

Simplify the equation:

\[ 4x = 48 \]

Now, solve for \( x \):

\[ x = \frac{48}{4} \]
\[ x = 12 \]

Thus, the length of the shorter piece is \( 12 \) inches. Since the longer piece is three times the length of the shorter piece:

\[ 3x = 3 \times 12 = 36 \]

Therefore, the lengths of the two pieces of ribbon are:
- The shorter piece: \( 12 \) inches
- The longer piece: \( 36 \) inches

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. If the total length of the ribbon was 60 inches, what would the lengths of the two pieces be?
2. How would the problem change if one piece was four times as long as the other?
3. What if the ribbon was divided into three pieces, with the lengths in the ratio 1:2:3?
4. How can you express the lengths of the two pieces algebraically if the total length was \( L \) inches?
5. What would be the length of each piece if the longer piece was five times the length of the shorter one?
6. Can we generalize this problem to any ratio between the lengths of the two pieces?
7. What if the total length of the ribbon was a variable \( L \) and the ratio of the two pieces was \( m:n \)?
8. How would the problem change if instead of cutting a ribbon, you were cutting a rope into two pieces?

Tip: When solving problems involving ratios and total amounts, setting up an equation based on the given conditions and solving for the unknown can simplify the process and lead to the correct solution efficiently.

Learn how to divide a 48-inch ribbon into two pieces, where one piece is three times as long as the other. Follow the step-by-step solution to find the lengths of each piece using algebraic equations. Suitable for students in Grades 5-7.

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