Question

the glee club has 120 cupcakes to sell. they have decided to arrange the cupcakes in the shape of a rectangle, such that the rows have an even number of cupcakes and the columns have an odd number of cupcakes. How many arrangements of cupcakes can they create?  Explain.

Answer 1

Here are the only ones I can think of that have only one even number and one odd number.

8 x 15
5 x 24
3 x 40

I simply used a calculator and did 120/1, 120/2, 120/3 etc.. and found these numbers that work together.

Answer 2

Answer: 4

Step-by-step explanation:

1) Find the divisors of 120:

1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 20, 30, 40, 60, and 120.

2) Choose combinations of even numbers for the rows and odd number for the columns:

row ------ column

8 ---------- 15 ----- ↔ 8 × 15 = 120

24 -------- 5 ------ ↔ 24 × 5 = 120

40 -------- 3 ------ ↔ 40 × 3 = 120

120 ------ 1 -------- ↔ 120 × 1 = 120

Those are the only arrangements with an even number of rows and odd number of columns: 4 in total.