A florist has 36 roses, 27 tulips, and 18 carnations she must use to create bouquets. Each bouquet must have an equal number of each type of flower as the other bouquets. What is the largest number of bouquets she can make without having any flowers left over? How many roses will be in each bouquet? How many tulips will be in each bouquet? How many carnations will be in each bouquet?(4 points)
Bouquets
In order to find the largest number of bouquets she can make without having any flowers left over, we need to find the common factor of 36, 27, and 18.
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, and 36.
The factors of 27 are: 1, 3, 9, and 27.
The factors of 18 are: 1, 2, 3, 6, 9, and 18.
The common factor for all three numbers is 3.
Therefore, she can make the largest number of bouquets without any flowers left over is 3.
To find out how many roses will be in each bouquet, we divide the total number of roses (36) by the number of bouquets (3).
36 roses ÷ 3 bouquets = 12 roses per bouquet.
To find out how many tulips will be in each bouquet, we divide the total number of tulips (27) by the number of bouquets (3).
27 tulips ÷ 3 bouquets = 9 tulips per bouquet.
To find out how many carnations will be in each bouquet, we divide the total number of carnations (18) by the number of bouquets (3).
18 carnations ÷ 3 bouquets = 6 carnations per bouquet.
Therefore, each bouquet will have 12 roses, 9 tulips, and 6 carnations.
To find the largest number of bouquets the florist can make without having any flowers left over, we need to find the common factor of the number of each type of flower.
The common factor of 36, 27, and 18 is 9.
Therefore, the florist can make 9 bouquets.
To find how many roses will be in each bouquet, we divide the total number of roses (36) by the number of bouquets (9).
36 / 9 = 4
So, each bouquet will have 4 roses.
Similarly, to find how many tulips and carnations will be in each bouquet, we divide the total number of tulips (27) and carnations (18) by the number of bouquets (9).
27 / 9 = 3
So, each bouquet will have 3 tulips.
18 / 9 = 2
Thus, each bouquet will have 2 carnations.
In summary:
- The florist can make 9 bouquets.
- Each bouquet will have 4 roses.
- Each bouquet will have 3 tulips.
- Each bouquet will have 2 carnations.
To determine the largest number of bouquets the florist can make without having any flowers left over, we need to find the greatest common divisor (GCD) of the numbers 36, 27, and 18. The GCD will represent the maximum number of bouquets.
To find the GCD, we can use the Euclidean algorithm, which involves finding the remainder when dividing the larger number by the smaller number. We repeat this process until we have a remainder of zero.
Let's find the GCD of 36 and 27 first:
- Divide 36 by 27: 36 ÷ 27 = 1 remainder 9
- Since the remainder is non-zero (9), we need to divide 27 by the remainder: 27 ÷ 9 = 3 remainder 0
Therefore, the GCD of 36 and 27 is 9.
Now, let's find the GCD of 9 and 18:
- Divide 18 by 9: 18 ÷ 9 = 2 remainder 0
Therefore, the GCD of 9 and 18 is 9.
Finally, we find the GCD of 9 and 9:
- Since both numbers are the same (9), the GCD is also 9.
So, the largest number of bouquets the florist can make without having any flowers left over is 9. Each bouquet will have an equal number of roses, tulips, and carnations.
To find out how many roses, tulips, and carnations will be in each bouquet, we divide the total number of each flower by the number of bouquets:
- Roses per bouquet = 36 / 9 = 4
- Tulips per bouquet = 27 / 9 = 3
- Carnations per bouquet = 18 / 9 = 2
Therefore, each bouquet will have 4 roses, 3 tulips, and 2 carnations.