2008 AMC 10B Problem 1

Question

A basketball player made

5

baskets during a game. Each basket was worth either

2

or

3

points. How many different numbers could represent the total points scored by the player?

2

3

4

5

6

If

k

baskets are worth

3

points, the total is

2(5-k)+3k

As

k

runs from

0

to

5

, the total increases by

1

each time

If

k

of the baskets are worth

3

points and the rest worth

2,

the total is

2(5-k)+3k=10+k.

As

k

ranges over

0,1,\ldots,5,

the total takes every integer value from

10

to

15,

giving

6

possibilities.

Thus, the correct answer is E.

Problem 1 in other years