Question
Beth wrote a system of equations to determine when a referee will earn the same salary working the East Conference and West Conference games.
y=40x−25
y=35x−5
Where x is the total number of games and y is the amount earned.
Beth determined that at 135 games, the referee would earn the same salary of $4 for each conference game, Is she correct?
(1 point)
Responses
No, she only estimated and did not find the exact values.
No, she only estimated and did not find the exact values.
No, she interpreted the solution of (4, 135) incorrectly.
No, she interpreted the solution of (4, 135) incorrectly.
No, she did not find the correct intersections point.
No, she did not find the correct intersections point.
Yes, Beth is correct.
Yes, Beth is correct.
y=40x−25
y=35x−5
Where x is the total number of games and y is the amount earned.
Beth determined that at 135 games, the referee would earn the same salary of $4 for each conference game, Is she correct?
(1 point)
Responses
No, she only estimated and did not find the exact values.
No, she only estimated and did not find the exact values.
No, she interpreted the solution of (4, 135) incorrectly.
No, she interpreted the solution of (4, 135) incorrectly.
No, she did not find the correct intersections point.
No, she did not find the correct intersections point.
Yes, Beth is correct.
Yes, Beth is correct.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if Beth is correct, we need to find when the referee earns the same salary for both conference games. We can do this by setting the equations equal to each other.
The equations are:
1. \( y = 40x - 25 \) (East Conference games)
2. \( y = 35x - 5 \) (West Conference games)
Set the equations equal to each other:
\[ 40x - 25 = 35x - 5 \]
Now, solve for x:
1. Subtract \( 35x \) from both sides:
\[ 40x - 35x - 25 = -5 \]
\[ 5x - 25 = -5 \]
2. Add 25 to both sides:
\[ 5x = 20 \]
3. Divide by 5:
\[ x = 4 \]
Now, we substitute \( x = 4 \) back into one of the original equations to find \( y \):
Using either equation, let's substitute into the first one:
\[ y = 40(4) - 25 \]
\[ y = 160 - 25 \]
\[ y = 135 \]
Thus, the solution is \( (4, 135) \) indicating that after 4 games, the referee earns $135.
Now, to evaluate Beth's claim:
- Beth stated that at 135 games, the referee would earn the same salary of $4 for each conference game. However, the calculation shows that when they play a total of 4 games, they earn $135, not at 135 games.
Given this information, the correct response is:
**No, she interpreted the solution of (4, 135) incorrectly.**
The equations are:
1. \( y = 40x - 25 \) (East Conference games)
2. \( y = 35x - 5 \) (West Conference games)
Set the equations equal to each other:
\[ 40x - 25 = 35x - 5 \]
Now, solve for x:
1. Subtract \( 35x \) from both sides:
\[ 40x - 35x - 25 = -5 \]
\[ 5x - 25 = -5 \]
2. Add 25 to both sides:
\[ 5x = 20 \]
3. Divide by 5:
\[ x = 4 \]
Now, we substitute \( x = 4 \) back into one of the original equations to find \( y \):
Using either equation, let's substitute into the first one:
\[ y = 40(4) - 25 \]
\[ y = 160 - 25 \]
\[ y = 135 \]
Thus, the solution is \( (4, 135) \) indicating that after 4 games, the referee earns $135.
Now, to evaluate Beth's claim:
- Beth stated that at 135 games, the referee would earn the same salary of $4 for each conference game. However, the calculation shows that when they play a total of 4 games, they earn $135, not at 135 games.
Given this information, the correct response is:
**No, she interpreted the solution of (4, 135) incorrectly.**
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