Abasketball team scored 31 points. the points were made up of three-pointers (3 points), feild goals (2 points), and foul shots (1 point). how many different ways could the team have scored 31 points?

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.

Step-by-step explanation:

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ci

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4