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

17

Explanation:

Alright, I am going to make this as simple as possible.

if you are doing this then you should know what the Greatest Common Factor means (GCF). First, find the factors of each:

40: 1,2,4,5,8,10,20

28: 1,2,4,7,14,28

Alright, so right off the bat you see you have three common factors: 1, 2 and 4

The greatest one is 4 so that one is the one we are going to use. (greatest common factor)

Now, because we are going to put those 40 and 28 flowers into rows of 4, then we have to divide them by 4.

So it would be 40 divided by 4 equals 10. So 4 rows of 10 flowers for the orange ones.

Visual representation:

_ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _

_ _ _ _ _ _ _ _ _ _

(4 rows of 10 each)

For the yellow ones, you would do the same: 28 divided by 4 equals 7.

Visual representation:

_ _ _ _ _ _ _

_ _ _ _ _ _ _

_ _ _ _ _ _ _

_ _ _ _ _ _ _

(4 rows of 7)

So now that you know you have 10 rows of orange flowers, and 7 rows of yellow flowers, you can add the rows to see how many rows in total there are. 10+7=17

So 17 rows in total.

Answer 2

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

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.