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

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

Answer 1

To sort the jerseys, the coach should use the distributive property of multiplication over addition and the greatest common factor (GCF). The GCF of 24 and 30 is 6.

To find the number of blue jerseys in each group, you can divide 24 by 6, which gives you 4. Similarly, dividing 30 by 6 gives you 5, which is the number of red jerseys in each group.

Now, to use the distributive property, you can multiply the GCF by the sum of the divided values. So, the answer is:

6(9 + 4)

Answer 2

To solve this problem, we need to find the greatest common factor (GCF) of 24 and 30, which is 6. The GCF is the largest number that divides both 24 and 30 evenly.

Now, let's use the Distributive Property of multiplication over addition to create equal groups of blue and red jerseys.

Option 1: 3(27+12)

To find out if this is a valid solution, let's break it down step by step.

Step 1: 27 + 12 = 39
Step 2: 3(39) = 117

Since 117 is not equal to the total number of jerseys (54), this option is not correct.

Option 2: 6(9 x 4)

Again, let's break it down step by step.

Step 1: 9 x 4 = 36
Step 2: 6(36) = 216

Since 216 is not equal to the total number of jerseys (54), this option is not correct either.

Option 3: 2(27 + 12)

Step 1: 27 + 12 = 39
Step 2: 2(39) = 78

Since 78 is not equal to the total number of jerseys (54), this option is also incorrect.

Option 4: 6(9 + 4)

Step 1: 9 + 4 = 13
Step 2: 6(13) = 78

Since 78 is equal to the total number of jerseys (54), this option is the correct answer.

Therefore, the coach should sort the jerseys into six groups, where each group consists of 9 blue jerseys and 4 red jerseys.