A soccer coach has 54 jerseys, of which 24 are blue and 30 are red. He wants to sort the jerseys so that each group has both colors of jersey. The coach also wants each group to have an equal number of blue jerseys and an equal number of red jerseys. Which answer best shows how the coach should sort the jerseys using the GCF and the Distributive Property of multiplication over addition? PAR 6.5

Question

A soccer coach has 54 jerseys, of which 24 are blue and 30 are red. He wants to sort the jerseys so that each group has both colors of jersey. The coach also wants each group to have an equal number of blue jerseys and an equal number of red jerseys. Which answer best shows how the coach should sort the jerseys using the GCF and the Distributive Property of multiplication over addition? PAR 6.5

responses

3(27+12)
6(9 x 4)
2(27 + 12)
6(9 + 4)

Answer 1

The correct answer is 2(27 + 12).

To use the GCF and the Distributive Property, we need to find the greatest common factor of 24 and 30, which is 6.

First, we can divide both numbers by 6 to simplify the problem: 24/6 = 4 and 30/6 = 5.

Now we can set up the equation using the Distributive Property:

2(4(7) + 5(6))

Simplifying the equation, we get:

2(28 + 30)

2(58)

So, the coach should sort the jerseys using the GCF and the Distributive Property as 2(27 + 12).