The table shows the number of points scored by three players in last night's basketball game. If Ray and Bill scored the same number of points, how many did John score?
| Player | Points |
|--------|-----------|
| John | [tex]x[/tex] |
| Ray | [tex]3x - 6[/tex] |
| Bill | [tex]4x - 10[/tex] |
Given that Ray and Bill scored the same number of points:
\[ 3x - 6 = 4x - 10 \]
Solve for [tex]x[/tex] to determine John's score.
Answer (3)
John scored 4 points. Here's how to solve this: Set the eqations of Ray and Bill equal to eachother and solve for x
3 x − 6 = 4 x − 10 3 x = 4 x − 4 − x = − 4 x = 4
John scored 4 points.
We are given the number of points scored by three basketball players with each player's points being a function of a variable x. Ray and Bill scored the same number of points, so we set their point functions equal to each other and solve for x.
Set Ray's points equal to Bill's points: 3x - 6 = 4x - 10.
Bring variables to one side and constants to the other: x = 4.
John scored x points, so if x = 4, then John scored 4 points.
John scored 4 points based on the equation derived from Ray and Bill's points. By setting their scores equal and solving for x, we found that x equals 4. Therefore, John's score is the same as the value of x, which is 4.
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