Question

Below is a new distance with given lengths to help Cecil cross the tightrope. Find at least two ways to get Cecil across. Write your solutions as numerical expressions.

b. Span of tightrope: 23 feet
Given lengths: 11, 13, 7 feet

Answer 1

To help Cecil cross a 23-foot tightrope, two methods involve either adding the lengths of two ropes (13 + 11 feet) or all three given ropes (11 + 13 + 7 feet). If the rope lengths are doubled, the numerical expressions become (2 × 13) + (2 × 11) and (2 × 11) + (2 × 13) + (2 × 7), both providing sufficient length for Cecil to cross the tightrope.

Step-by-step explanation:

The student is asked to find numerical expressions to help Cecil cross a tightrope of 23 feet using given rope lengths of 11, 13, and 7 feet. To solve for two ways Cecil can cross, we can consider joining the ropes to meet or exceed the span of the tightrope.

• Method 1: Adding the lengths of two ropes. For instance, 13 feet + 11 feet = 24 feet, which is longer than the span of the tightrope, allowing Cecil to cross. The numerical expression for this method is 13 + 11.
• Method 2: Adding all three rope lengths. By adding 11 feet + 13 feet + 7 feet, we get a total length of 31 feet, also sufficient for Cecil to cross the tightrope. The numerical expression for this method is 11 + 13 + 7.

However, the problem also requires us to consider the situation where twice the length of nylon rope is used, which can be depicted numerically by multiplying each length by two before proceeding with the addition.

• Method 1 with doubled lengths: (2 × 13) + (2 × 11) = 26 + 22 = 48 feet.
• Method 2 with doubled lengths: (2 × 11) + (2 × 13) + (2 × 7) = 22 + 26 + 14 = 62 feet.

This demonstrates that with doubled rope lengths, Cecil can easily cross the tightrope using either method.