Question

Stacy is planning a vegetable garden. She has 27 tomato plants,45 bean plants, and 54 carrot plants. Stacy wants each row of hergarden to have the same number of each type of plant. What is thegreatest number of rows that Stacy can have if she wants to use allof her plants? How many of each type of plant will she have ineach row?Show your work.

Answer 1

To determine the number of rows we need to determine the Greatest Common

Factor (GCF) between the numbers of each of the plants Stacy has, this means that we need to determine GCF (27, 45, 54). This means that we need to find the greatest number that can divide these number with a remainder of zero.

To determine the GCF, we will determine the factor of each of the numbers.

For 27 we have:

`Factors\text{ of 27 =1, 3, }9,\text{ 27}`

For 45 we have:

`\text{Factors of 45 = }1,3,5,9,15,45`

For 54 we have:

`\text{Factors of 54 = 1, }2,3,6,9,18,27,54`

The greatest common factor between the three numbers is 9. Therefore, the maximum number of rows is 9.

Now, to determine the number of plants on each row we divide the total number of plants by the GCF.

For the 27 tomatoes we have:

`T=(27)/(9)=3`

For the 45 beans:

`B=(45)/(9)=5`

For the 54 carrots:

`C=(54)/(9)=6`

Therefore, Stacy must have 9 rows and each row must contain 3 tomato plants, 5 bean plants, and 6 carrot plants.