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?
To determine the largest number of bouquets she can make without having any flowers left over, we need to find the greatest common divisor of the number of each type of flower:
GCD(36, 27, 18) = 9
So, she can make a maximum of 9 bouquets.
To find out how many roses will be in each bouquet, we divide the total number of roses by the number of bouquets:
36 roses ÷ 9 bouquets = 4 roses per bouquet
So, there will be 4 roses in each bouquet.
Similarly, for tulips:
27 tulips ÷ 9 bouquets = 3 tulips per bouquet
So, there will be 3 tulips in each bouquet.
And for carnations:
18 carnations ÷ 9 bouquets = 2 carnations per bouquet
So, there will be 2 carnations in each bouquet.
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To determine the largest number of bouquets she can make without having any flowers left over, we need to find the greatest common divisor of the number of each type of flower:
GCD(36, 27, 18) = 9
So, she can make a maximum of 9 bouquets.
To find out how many roses will be in each bouquet, we divide the total number of roses by the number of bouquets:
36 roses ÷ 9 bouquets = 4 roses per bouquet
So, there will be 4 roses in each bouquet.
Similarly, for tulips:
27 tulips ÷ 9 bouquets = 3 tulips per bouquet
So, there will be 3 tulips in each bouquet.
And for carnations:
18 carnations ÷ 9 bouquets = 2 carnations per bouquet
So, there will be 2 carnations in each bouquet.
Therefore, the largest number of bouquets she can make without having any flowers left over is 9. Each bouquet will have 4 roses, 3 tulips, and 2 carnations.
To find the largest number of bouquets she can make without any flowers left over, we need to find the greatest common divisor (GCD) of 36, 27, and 18.
Step 1: Find the GCD of 36 and 27:
- The prime factors of 36 are 2^2 * 3^2.
- The prime factors of 27 are 3^3.
- The common prime factor is 3^2.
- So, the GCD of 36 and 27 is 3^2 = 9.
Step 2: Find the GCD of 9 and 18:
- The prime factors of 9 are 3^2.
- The prime factors of 18 are 2 * 3^2.
- The common prime factor is 3^2.
- So, the GCD of 9 and 18 is 3^2 = 9.
Therefore, the largest number of bouquets the florist can make without having any flowers left over is 9.
To find the number of roses, tulips, and carnations in each bouquet, we divide the total number of each flower by the number of bouquets:
Number of roses in each bouquet = Total number of roses / Number of bouquets
Number of tulips in each bouquet = Total number of tulips / Number of bouquets
Number of carnations in each bouquet = Total number of carnations / Number of bouquets
Number of roses in each bouquet = 36 / 9 = 4
Number of tulips in each bouquet = 27 / 9 = 3
Number of carnations in each bouquet = 18 / 9 = 2
Therefore, each bouquet will have 4 roses, 3 tulips, and 2 carnations.
To find the largest number of bouquets the florist can make without any flowers left over, we need to determine the greatest common divisor (GCD) of the given numbers - 36, 27, and 18.
Step 1: Find the GCD of 36 and 27.
To find the GCD, we can use the Euclidean algorithm.
Divide 36 by 27:
36 ÷ 27 = 1 remainder 9
Then divide 27 by the remainder:
27 ÷ 9 = 3.
Since the remainder is zero, the GCD of 36 and 27 is 9.
Step 2: Find the GCD of 9 and 18.
Divide 18 by 9:
18 ÷ 9 = 2.
Again, the remainder is zero, so the GCD of 9 and 18 is 9.
Step 3: Find the GCD of 9 (the GCD of the previous step) and 9 (the GCD of the first step).
Since both numbers are the same, the GCD is 9.
Therefore, the largest number of bouquets the florist can make without any flowers left over is 9.
To figure out how many roses, tulips, and carnations will be in each bouquet, we divide the total number of each flower type by the number of bouquets.
Number of roses in each bouquet:
36 roses ÷ 9 bouquets = 4 roses per bouquet.
Number of tulips in each bouquet:
27 tulips ÷ 9 bouquets = 3 tulips per bouquet.
Number of carnations in each bouquet:
18 carnations ÷ 9 bouquets = 2 carnations per bouquet.
So, in each bouquet, there will be 4 roses, 3 tulips, and 2 carnations.