Question

1. higher order thinking the difference between the longest worm and the shortest worm was $1\frac{1}{2}$ inches. the shortest worm was $3\frac{1}{4}$ inches long. there were 2 worms that were $4\frac{1}{4}$ inches long. find the length of the longest worm.

Explanation:

Step1: Define variable for longest worm

Let $L$ = length of longest worm (in inches).

Step2: Set up difference equation

The difference between longest and shortest is given by $L - 1\frac{2}{4} = 3\frac{1}{4}$.
First convert mixed numbers to improper fractions:
$1\frac{2}{4} = \frac{6}{4}$, $3\frac{1}{4} = \frac{13}{4}$
Equation becomes: $L - \frac{6}{4} = \frac{13}{4}$

Step3: Solve for $L$

Add $\frac{6}{4}$ to both sides:
$L = \frac{13}{4} + \frac{6}{4} = \frac{19}{4}$
Convert back to mixed number: $\frac{19}{4} = 4\frac{3}{4}$

Answer:

$4\frac{3}{4}$ inches