Answer :
Answer:
To determine the number of people each bus can carry, let's denote:
- \( S \) as the number of people a small bus can carry.
- \( L \) as the number of people a large bus can carry.
We have the following two equations based on the given information:
1. \( 7S + 5L = 331 \)
2. \( 4S + 9L = 398 \)
We can solve this system of equations using either substitution or elimination. Let's use the elimination method.
First, we will eliminate one of the variables by making the coefficients of \( S \) or \( L \) the same in both equations. Let's eliminate \( S \).
To do this, we will multiply the first equation by 4 and the second equation by 7 to make the coefficients of \( S \) the same:
\[ 4(7S + 5L) = 4(331) \]
\[ 28S + 20L = 1324 \]
\[ 7(4S + 9L) = 7(398) \]
\[ 28S + 63L = 2786 \]
Now we subtract the first new equation from the second new equation to eliminate \( S \):
\[ (28S + 63L) - (28S + 20L) = 2786 - 1324 \]
\[ 43L = 1462 \]
Solving for \( L \):
\[ L = \frac{1462}{43} \]
\[ L = 34 \]
Now that we have \( L \), we can substitute it back into one of the original equations to solve for \( S \). Let's use the first equation:
\[ 7S + 5L = 331 \]
\[ 7S + 5(34) = 331 \]
\[ 7S + 170 = 331 \]
\[ 7S = 331 - 170 \]
\[ 7S = 161 \]
\[ S = \frac{161}{7} \]
\[ S = 23 \]
Therefore, the number of people each bus can carry is:
- Each small bus can carry 23 people.
- Each large bus can carry 34 people.
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Answer:
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