Yolanda buys two types of flowering plants. She buys 36 geraniums and 63 marigolds she wants to plant an eeach row will contain only one type of flowering each row will contain only one type of flowering plant 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
They both have a greatest common factor of 9 so the greatest number of plants in each row is 9. Then there are 4 rows of geraniums (4•9=36) and 7 rows of marigolds (7•9=63). Good luck!
Well, Yolanda certainly has quite the green thumb! Now, let's see if we can figure out the greatest number of flowering plants that could be in each row of her garden.
Since Yolanda wants each row to contain only one type of flowering plant, we need to find the common factors of 36 and 63. Let me put on my funny mathematician hat and do some quick calculations.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
And the factors of 63 are: 1, 3, 7, 9, 21, 27, and 63.
To find the greatest number that could be in each row, we need to find the highest common factor of 36 and 63, which in this case is 9.
So, the greatest number of flowering plants that could be in each row of Yolanda's garden is 9. That's a blooming good number, don't you think?
To determine the greatest number of flowering plants that could be in each row of the garden, we need to find the greatest common divisor (GCD) of the number of geraniums (36) and marigolds (63) that Yolanda bought.
The GCD is the largest number that divides evenly into both numbers. To find the GCD, we can use the Euclidean algorithm, which involves dividing the larger number by the smaller number and then taking the remainder. We repeat this process, dividing the previous divisor by the new remainder, until the remainder is zero. The last non-zero remainder is the GCD.
Let's apply the Euclidean algorithm:
Step 1: Divide 63 (larger number) by 36 (smaller number).
63 ÷ 36 = 1 with a remainder of 27.
Step 2: Divide the previous divisor (36) by the remainder (27).
36 ÷ 27 = 1 with a remainder of 9.
Step 3: Divide the previous divisor (27) by the remainder (9).
27 ÷ 9 = 3 with no remainder.
Since the remainder is now zero, the GCD is 9.
Therefore, the greatest number of flowering plants that could be in each row of the garden is 9.