Question 655017: A Basketball team scored 87 points in 2 point and 3 point baskets. If the 2 point baskets had been 3 point baskets, and the 3 point baskets had been 2 points, the team would have scored 93 points. Find how many 2 point baskets and how many 3 point baskets the team scored.
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A Basketball team scored 87 points in 2 point and 3 point baskets. If the 2 point baskets had been 3 point baskets, and the 3 point baskets had been 2 points, the team would have scored 93 points. Find how many 2 point baskets and how many 3 point baskets the team scored.
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Let x = number of 2-point baskets
and y = number of 3-point baskets
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Because we have two unknowns, we need to find two equations:
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From: "A Basketball team scored 87 points in 2 point and 3 point baskets." we get:
2x + 3y = 87 (equation 1)
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And from: "If the 2 point baskets had been 3 point baskets, and the 3 point baskets had been 2 points, the team would have scored 93 points" we get:
2y + 3x = 93 (equation 2)
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solve equation 1 for y:
2x + 3y = 87
3y = 87-2x
y = 29-(2/3)x
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substitute above into equation 2 to solve for x:
2y + 3x = 93
2(29-(2/3)x) + 3x = 93
58-(4/3)x + 3x = 93
-(4/3)x + 3x = 35
-4x + 9x = 105
5x = 105
x = 21 (number of 2-point baskets)
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To find number of 3-point baskets, substitute back into equation 1:
2x + 3y = 87
2(21) + 3y = 87
42 + 3y = 87
3y = 45
y = 15
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