Question

Mathcounts: Grace made over four dozen cupcakes. If she makes packages of 2 cupcakes, then there is 1 left over. Packaging in groups of 3 cupcakes leaves 2 left over,

and packaging in groups of 4 cupcakes leaves 3 left over. What is the fewest
number of cupcakes Grace could have made?

Answer 1

Answer: 59

Explanation:

48/2=24

24-3=21

21/7=3

3*19.9999999999997=59

Answer 2

Explanation:

4 dozen = 48 cupcakes

The number must be odd over 48

Number must be multiple of 3 + 2

so:

With the number x:
x = 2a + 1 = 3b + 2 = 4c + 3 =?

2a + 1 = 3b + 2 = 4c + 3

2a + 1 = 59

3b + 2 = 59

4c + 3 = 59