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Sagot :
To determine who is correct between Zaid and Marcus, we need to compare the total amount of leftover parts of the three snacker bars to one whole snacker bar.
Let’s assume that each snacker bar is divided into equal parts for ease of calculation.
### Step 1: Represent how much each person has eaten.
1. Zaid has eaten \(\frac{2}{3}\) of his snacker bar.
2. Marcus has eaten \(\frac{3}{4}\) of his snacker bar.
3. You have eaten \(\frac{5}{6}\) of your snacker bar.
### Step 2: Calculate the leftover parts.
1. **Zaid’s leftover part**:
\[
1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{1}{3}
\]
2. **Marcus’s leftover part**:
\[
1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}
\]
3. **Your leftover part**:
\[
1 - \frac{5}{6} = \frac{6}{6} - \frac{5}{6} = \frac{1}{6}
\]
### Step 3: Add the leftover parts together.
To add these fractions, we need a common denominator. The least common multiple of 3, 4, and 6 is 12.
1. Convert \(\frac{1}{3}\) to twelfths:
\[
\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}
\]
2. Convert \(\frac{1}{4}\) to twelfths:
\[
\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}
\]
3. Convert \(\frac{1}{6}\) to twelfths:
\[
\frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12}
\]
Now add these fractions:
\[
\frac{4}{12} + \frac{3}{12} + \frac{2}{12} = \frac{9}{12}
\]
### Step 4: Compare the total with one whole snacker bar.
The total leftover parts:
\[
\frac{9}{12} = \frac{3}{4}
\]
### Conclusion
Since \(\frac{3}{4}\) is less than 1 whole snacker bar, the total leftover parts of the three snacker bars do not add up to more than one whole snacker bar.
Therefore, Marcus is correct. The leftover parts of the three snacker bars altogether would not be more than a whole snacker bar.
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