Question

type of flower amount
lilies 60
daisies 36
carnations 22
roses 47
tulips 24
the florist makes the greatest number of identical arrangements with the lilies and the daisies. which combination describes the arrangements? 6 arrangements with 10 lilies and 6 daisies 6 arrangements with 6 lilies and 10 daisies 12 arrangements with 10 lilies and 6 daisies 12 arrangements with 5 lilies and 3 daisies

Explanation:

Step1: Find GCD of 60 and 36

We need to find the greatest - common divisor (GCD) of the number of lilies (60) and daisies (36) to get the greatest number of identical arrangements. Using the Euclidean algorithm:
$60 = 36\times1 + 24$
$36=24\times1 + 12$
$24 = 12\times2+0$. So, $\gcd(60,36)=12$.

Step2: Calculate number of lilies and daisies per arrangement

Number of lilies per arrangement: $\frac{60}{12}=5$
Number of daisies per arrangement: $\frac{36}{12}=3$

Answer:

12 arrangements with 5 lilies and 3 daisies