Roberto has 150 roses, 120 lilies, and 60 hydrangeas to make bouquets. Each bouquet should have the same number of each type of flower.b) How many roses, lilies, and hydrangeas will be in each bouquet?
GCF(150,120,60) = 30
So, you can make 30 bundles, each with 5 roses, 4 lilies, 2 hydrangeas
To determine the number of roses, lilies, and hydrangeas in each bouquet, we need to find the greatest common divisor (GCD) of the given numbers.
The GCD is the largest number that divides all the given numbers without leaving a remainder. We can use the Euclidean algorithm to easily find the GCD.
Let's find the GCD of 150, 120, and 60:
1. Start with the two largest numbers, 150 and 120.
150 = 1 * 120 + 30
2. Now take the previous divisor (120) as the new dividend and the remainder (30) as the new divisor.
120 = 4 * 30 + 0
3. We reached a remainder of 0, which means that the divisor (30) is the GCD.
Therefore, the GCD of 150, 120, and 60 is 30.
Since each bouquet should have an equal number of each flower, we divide each number of flowers by the GCD:
150 / 30 = 5
120 / 30 = 4
60 / 30 = 2
So, each bouquet will have:
- 5 roses
- 4 lilies
- 2 hydrangeas.