To solve the problem, we can start by understanding the ratio of Emily's crackers to Jake's, which is 2:3. This means for every 2 crackers Emily has, Jake has 3 crackers.
First, let's denote Emily's crackers as \( E \) and Jake's crackers as \( J \).
According to the ratio:
\[ \frac{E}{J} = \frac{2}{3} \]
This can be expressed in terms of a common variable \( x \):
\[ E = 2x \quad \text{and} \quad J = 3x \]
Next, we know the total number of crackers is 30, so we can write the equation:
\[ E + J = 30 \]
Substituting the expressions for \( E \) and \( J \):
\[ 2x + 3x = 30 \]
Combining the terms gives:
\[ 5x = 30 \]
Now, solving for \( x \):
\[ x = \frac{30}{5} = 6 \]
Now that we have \( x \), we can find the number of crackers each person has:
For Emily:
\[ E = 2x = 2 \times 6 = 12 \]
And for Jake:
\[ J = 3x = 3 \times 6 = 18 \]
Now, to check our work:
- The total number of crackers: \( E + J = 12 + 18 = 30 \) (correct)
- The ratio \( \frac{E}{J} = \frac{12}{18} = \frac{2}{3} \) (correct)
Thus, Emily has \( \boxed{12} \) crackers.
Tape Diagram:
To visualize this using a tape diagram, we can represent the crackers with segments:
- Draw 5 equal segments in a row (these represent the total of 5 parts in the ratio),
- Color 2 segments to represent Emily’s 2 parts,
- Color 3 segments to represent Jake’s 3 parts.
This would visually show that Emily has 2 out of the total 5 parts, which helps reinforce the calculation. Each segment would represent \( 6 \) crackers (since \( x = 6 \)). Thus, Emily has \( 12 \) crackers, and Jake has \( 18 \) crackers.