Question 622631: During the second game of the 2002 Western Conference finals, the Los Angeles Lakers scored a total of 90 points, resulting from a combination of three-point baskets, two-point baskets, and one-point free-throws. There were 11 times as many two-point baskets as three-point baskets and five times as many free-throws as three-point baskets. What combination of scoring accounted for the Lakers 90 points?
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! Hi, there--
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We can solve this problem using algebra.
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Let x be the number the 1-point free throws.
let y be the number of 2-point shots.
let z be the numb of 3-point shots.
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Now we need to write three equations using the information in the problem to model this situation.
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The Lakers scored a total of 90 points, so the points from each type of shot must sum up to 90. Three-pointers are worth 3 times the number of shots, or 3z. Two-point baskets are worth two times the number of shots, or 2y. Free throws are worth 1 times the number of shots, or x. In algebra, we can write this as
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There were 11 times as many two-point baskets as three-point baskets. In other words,
[the number of 2-point baskets] = [11] * [the number of 3-point baskets].
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In algebra, we write this as
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There were five times as many free-throws as three-point baskets. In other words,
[the number of free throws] = [5] * [the number of 3-point baskets].
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In algebra, we write this relationship as,
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Now we have a system of three equations and three variables. We will solve for x, y, and z.
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We begin by using the substitution method. The third equation states that x=5z, so substitute 5z for x in the first equation.
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Simplify.
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The second equation states that y=11z, so substitute 11z for y.
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Solve for z.
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The Lakers made 3 three-point shots.
They made 11 times as many two-point shots, or 33 two-point shots.
They made 5 times as many free throws, or 15 free throws.
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We need to make sure that this scoring combination gave them a total of 90 points:
3 three-pointers give 9 points.
33 two-point shots give 66 points.
15 free throws give 15 points.
9+66+15 does equal 90 points all together.
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Tht's it. Feel free to email me if you have questions about any part of the explanation.
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Ms.Figgy
math.in.the.vortex@gmail.com
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