Solved on Nov 03, 2023
Find the greatest number of identical flower arrangements Lauren can make using roses and daisies, with no flowers left over.
STEP 1
Assumptions1. Lauren has49 roses.
. Lauren has28 daisies.
3. All the flower arrangements must be identical.
4. There should be no flowers left over after making the arrangements.
STEP 2
To make the flower arrangements identical and have no flowers left over, we need to find the greatest common divisor (GCD) of the number of roses and daisies. The GCD is the largest number that divides both numbers without leaving a remainder.
STEP 3
To find the GCD, we can use the Euclidean algorithm. This algorithm is based on the principle that the GCD of two numbers a and b is the same as the GCD of b and a % b, where % is the modulus operator.
First, we check if49 is divisible by28.
Since49 is not divisible by28, we take28 and the remainder21 and repeat the process.
STEP 4
Now, we check if28 is divisible by21.
Since28 is not divisible by21, we take21 and the remainder7 and repeat the process.
STEP 5
Now, we check if21 is divisible by7.
Since21 is divisible by7, we have found the GCD.
STEP 6
The GCD of49 and28 is. Therefore, the greatest number of identical flower arrangements Lauren can make is.
Lauren can make flower arrangements.
Was this helpful?
