Math Brain Teaser

Question

Katie and her friend Jackson went to the grocery store. Jackson bought 3 apples and 4 oranges. Katie bought apples, oranges, and bananas. She bought the same total number of fruits as Jackson. How many possible combinations of fruits could Katie have bought?

The answer is 17 combinations. Will you give me the list of combinations please!

Thanks,

John

(Teacher)

Answer 1

a+o+b = 7 fruit for Katie = a+o for Jackson = 7 fruit

a o b

1 1 5

1 2 4

1 3 3

1 4 2

1 5 1

2 1 4

2 2 3

2 3 2

2 4 1

3 1 3

3 2 2

3 3 1

4 1 2

4 2 1

5 1 1

5+4+3+2+1 = 15 ways if she buys at least 1 of each of the 3 fruits

if she bought 0 of a fruit then add in 15 more for total 15+15 =30

7 0 0

6 1 0

6 0 1

5 2 0

5 0 2

4 3 0

4 0 3

3 4 0

3 0 4

2 5 0

2 0 5

1 6 0

1 0 6

0 7 0

0 0 7 double 0 7 James Bond Ian Fleming

answer is 15, or 30 if you allow buying none of 1 or 2 of the fruits