Question

The local florist is making bouquets for a wedding. She has 36 roses, 24 irises, and 48 daisies. She wants each bouquet to have the same number of each type of flower with none left over. Which expression shows the greatest common factor of these three values using the distributive property?

A) 6(6 + 4 + 8)
B) 12(3+2+4)
C) 3(12+8+16)
D) 419 +6+12

Answer 1

To create bouquets with an equal number of each flower without leftovers, the greatest common factor (GCF) of the flowers is calculated, yielding 12(3 + 2 + 4) as the correct expression using the distributive property.

Step-by-step explanation:

The local florist is making bouquets for a wedding and needs to determine how many of each type of flower to include in each bouquet without leaving any flowers out. The florist has 36 roses, 24 irises, and 48 daisies.

To find an expression that shows the greatest common factor (GCF) of these three values using the distributive property, we first need to determine the GCF. The GCF of 36, 24, and 48 is 12. Then, using the distributive property, we divide each number of flowers by the GCF to see what the expression inside the parenthesis should be:

• 36 roses / 12 = 3 roses
• 24 irises / 12 = 2 irises
• 48 daisies / 12 = 4 daisies

Therefore, the expression representing the greatest common factor using the distributive property is 12(3 + 2 + 4), which matches option B.