During the third quarter of a basketball game between the Tigers and the Bears, four different players scored all of the points for the Tigers. Player A scored 1/2 of the Tigers points. Player B scored 1/3 of the Tigers points. Player C made one three-point basket. Player D scored the last point by sinking a free throw. How many points did the Tigers score in the third quarter?
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PRECALCULUS WORD PROBLEM EQUATIONS SYSTEM OF EQUATIONS SYSTEMS OF EQUATIONS BY ELIMINATION SYSTEMS WORD PROBLEM HELP WRITING AN EQUATION
Lobby D. asked • 12/01/14
System of Equations word problem I can't figure out!!!!
A basketball player scored 40 points in a game. The number of three-point field goals the player made was 22 less than three times the number of free throws (each worth 1 point). Twice the number of two point field goals the player made was 11 more than the number of three point field goals made. Find the number of free-throws, two point field goals, and three point field goals that the player made in the game.
Once I have the equations I understand how to do the problem, but I am obviously doing something wrong because each time I write out the equations I end up getting fractions.
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Bill P. answered • 12/19/14
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If you let x represent the number of free throws (worth 1 point each)
let y represent the number of two-point field goals (worth 2 points each)
let z represent the number of three-point shots made (worth 3 points each)
Then the correct system of linear equations is as follows:
x + 2y + 3z = 40 (The total number of points scored is 40.)
z = 3x - 22 (The number of 3-pointers was 22 less than 3 times the number of free throws.)
2y = z + 11 (Twice the number of 2-point shots made was 11 more than the number of 3-pointers.)
The solution is as follows:
This basketball player scored 9 points via free throws (9 at 1 point each), 16 points via 8 two-point shots made, and 15 points via 5 three-point shots made.
One should then re=read each statement presented in the paragraph to be sure that these numbers make a true statement out of every one of the sentences in this paragraph. I checked them and they do ! My method to solve this was to utilize row-reduced echelon form, a technique a learned in college about 40 years ago. (After i dusted it off, of course.)