Question
Part 1 of 2
A player scored 94 points in a single professional basketball game. He made a total of 58 baskets, consisting of field 15 points
goals (worth two points) and foul shots (worth one point). Find the number of field goals and the number of foul shots
that the player made.
A player scored 94 points in a single professional basketball game. He made a total of 58 baskets, consisting of field 15 points
goals (worth two points) and foul shots (worth one point). Find the number of field goals and the number of foul shots
that the player made.
Ask by Ryan Lyons. in the United States
Nov 14,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
Field goals: 36, Foul shots: 22
Solution
Let
-
The total number of baskets made:
-
The total points scored:
Now, we can solve this system of equations.
First, we can solve the first equation for
Next, we substitute this expression for
Now, simplify the equation:
Now that we have
Thus, the player made:
- 36 field goals
- 22 foul shots
To summarize:
- Field goals:
- Foul shots:
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To tackle this exciting scoring mystery, let’s set up our equations! Let
-
For the total baskets:
-
For the total points:
Now, we can solve this system of equations. First, from the first equation, we can express
Next, substitute this equation into the second equation:
Simplifying this gives:
Now, solving for
Now, plugging
So the player made 36 field goals and 22 foul shots. Isn’t that an incredible scoring feat?
