Question

Cindi is planting a rectangular flower bed with 40 orange flower and 28 yellow flowers. She wants to plant them so that each row will have the same number of plants but of only one color. How many rows will Cindi need if she puts the greatest possible number of plants in each row?(show all work please)

Answer 1

Answer: 17 rows, 7 of yellow flowers and 10 of orange flowers.

Step-by-step explanation:

We have 40 orange flowers

we have 28 yellow flowers.

The total number of flowers is 40 + 28= 68

Now, we want to find the maximal comon factor between 28 and 40 (that will be the number of flowers in each row)

for this, we took the smallest number and find its factors, and then we see if those factors are also of the greater number.

28/1 = 28 ----> 40/28 is not integer, so 28 is not a factor of 40.

28/2 = 14 ----> 40/14 is not integer, so 14 is not a factor of 40.

28/3 is not integer.

28/4 = 7 ----> 40/7 is not integer, so 7 is not a factor of 40.

28/5 is not integer.

28/6 is not integer.

28/7 = 4, 40/4 = 10, so 4 is a factor of both 28 and 40.

Then the maximum number of flowers that we can put in each row is 4.

this means that we have:

28/4 = 7 rows of yellow flowers (with 4 flowers each)

40/4 = 10 rows of orange flowers (with 4 flowers each)

a total of 17 rows.