Question 832454: Quentin was challenged to a half-court shooting completion. For every half-court shot he makes, he will earn 20 points. For each half-court shot he misses, he will lose five points. After 20 half-court shots, Quentin has zero points. How many half-court shots did he make?
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website!
Hi, there--
THE PROBLEM:
Quentin was challenged to a half-court shooting completion. For every half-court shot he makes, he will
earn 20 points. For each half-court shot he misses, he will lose five points. After 20 half-court shots,
Quentin has zero points. How many half-court shots did he make?
A SOLUTION:
Let x be the number of half-court shots that Quentin makes.
Quentin has 20 attempts all together, so the number he misses will be 20 minus the number he makes,
or 20-x.
He earns 20 points for each shot he makes, or 20x all together.
He loses 5 points for every shot he misses, or -5(20-x) all together.
After 20 attempts, the sum of his points is 0, so
20x - 5(20-x) = 0
Solve for x to find the number of half court shots he made. Distribute the 5 to get rid of the parentheses.
20x - 100 + 5x = 0
Combine like terms. (20x+5x is 25x.)
25x - 100 = 0
Add 100 to both sides to combine constant terms. (-100+100 is 0.)
25x = 100
Divide both sides by 25 to isolate the variable. (25x/25 is x.)
25x/25 = 100/25
x = 4
In the context of this problem, x = 4 means that Quentin made 4 half-court shots.
Let's make sure that answer makes sense. Quentin gets 20 points for every shot he makes. So he earned
4*20=80 points. That left 16 misses because 20-4=16. He lost 5 points every time he missed. That's a
loss of 80 points because 16*5= 80. He earned 80 points and lost 80 points. After 2 attempts, his score is 0.
Hope this helps! Feel free to email if you have any questions about the solution.
Good luck with your math,
Mrs. F
math.in.the.vortex@gmail.com
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