Question

Jake and Emily both have crackers for a snack. The ratio of Emily's crackers to Jake's is 2:3. If there are 30 crackers total, how many crackers does Emily have? Use a tape diagram to help organize your thinking.

Answer 1

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.