Math  /  Numbers & Operations

QuestionQuestion 6
Yolanda buys two types of flowering plants. She buys 36 geraniums and 63 marigolds. She wants to plant an equal number of flowers in each row of her garden. Each row will contain only one type of flowering plant.
Part A
Yolanda uses all the plants she bought in her garden. Determine the greatest number of flowering plants that could be in each row of the garden. \square plants
Part B
How many rows of each type of flowering plant will be in Yolanda's garden? \square rows of geraniums \square rows of marigolds

Studdy Solution

STEP 1

1. Yolanda has bought 36 geraniums and 63 marigolds.
2. She wants each row to contain only one type of flowering plant.
3. Each row must have an equal number of plants.

STEP 2

1. Determine the greatest common divisor (GCD) of 36 and 63 to find the greatest number of flowering plants that could be in each row.
2. Use the GCD to determine the number of rows for each type of flowering plant.

STEP 3

Find the prime factorization of 36.
36=22×32 36 = 2^2 \times 3^2

STEP 4

Find the prime factorization of 63.
63=32×7 63 = 3^2 \times 7

STEP 5

Determine the GCD by finding the common prime factors with the lowest powers.
The common prime factor is 323^2.
GCD(36,63)=32=9 \text{GCD}(36, 63) = 3^2 = 9

STEP 6

Calculate the number of rows of geraniums. Since each row has 9 plants:
369=4 rows of geraniums \frac{36}{9} = 4 \text{ rows of geraniums}

STEP 7

Calculate the number of rows of marigolds. Since each row has 9 plants:
639=7 rows of marigolds \frac{63}{9} = 7 \text{ rows of marigolds}
Solution:
The greatest number of flowering plants that could be in each row of the garden is 99 plants.
Yolanda will have 44 rows of geraniums and 77 rows of marigolds.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord