Basketball

Question

Shaquille O'Neal scored his season high points 40. His 40 points were scored all on free throws and two-points baskets. He made a total of 25 shots. How many two point baskets did Shaq make.

Answer 1

Jokes about him making free throws aside, let t be the number of two point shots he made, and f be the number of free throws.

t + f = 25 total shots made, and we know he must have made at least one free throw because if he made 25 two-point shots he would have had 40 points.

 

2t  + f = 40 is the point value of all of his made shots.

 

You can use graphing methods, substitution, or linear combinations (elimination) to solve this system.

 

If we multiply the top equation by -1:

-t - f = -25

then add the bottom equation

-t - f = -25

2t + f = 40

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 t = 15, so he made 15 two point shots, for a subtotal of 30 points

 15 + f = 25, so he made 10 free throws, for a subtotal of 10 points

 

Now make sure this is consistent with the problem of 25 shots and 40 points