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Question
Mary scored a total of 27 points in a basketball game. During the game, all her points came from 3-point shots and 2-point shots. The number of 3-point shots she made is 4 more than her 2-point shots. How many 3-point shots and 2-point shots did she make?
Responses
A 2 three-point shots and 6 two-point shots2 three-point shots and 6 two-point shots
B 3 three-point shots and 7 two-point shots3 three-point shots and 7 two-point shots
C 6 three=point shots and 2 two-point shots6 three=point shots and 2 two-point shots
D 7 three-point shots and 3 two-point shots
Let's say the number of 2-point shots Mary made is x.
According to the problem, the number of 3-point shots Mary made is 4 more than her 2-point shots. So, the number of 3-point shots she made is x + 4.
The total number of points Mary scored from 2-point shots is 2x, and the total number of points she scored from 3-point shots is 3(x + 4).
The problem states that Mary scored a total of 27 points, so we can set up the equation:
2x + 3(x + 4) = 27
Simplifying the equation:
2x + 3x + 12 = 27
Combining like terms:
5x + 12 = 27
Subtracting 12 from both sides:
5x = 15
Dividing both sides by 5:
x = 3
So, Mary made 3 two-point shots.
The number of 3-point shots she made is 3 + 4 = 7.
Therefore, Mary made 7 three-point shots.
The correct answer is D) 7 three-point shots and 3 two-point shots.