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.

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.

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Edufirst Edufirst · Answer 2 · 2018-08-05T09:04:23-04:00

Answer: 4

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.