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)
The coach should sort the jerseys using the equation 2(27 + 12).
To solve this problem using the GCF (Greatest Common Factor) and the Distributive Property of multiplication over addition, we need to find the common factor between the numbers of blue (24) and red (30) jerseys.
The GCF of 24 and 30 is 6. This means that 6 is the largest number that divides both 24 and 30 evenly.
Now, let's use the Distributive Property to sort the jerseys.
Option 1: 3(27+12)
This means that we multiply the common factor (6) by the sum of the number of blue jerseys (24) and the number of red jerseys (30). Plugging in the values, it becomes:
3(24 + 30) = 3(54) = 162
Option 2: 6(9 x 4)
This option multiplies the common factor (6) by the product of factors of 24 and 30, which are 9 and 4, respectively. Plugging in the values:
6(9 x 4) = 6(36) = 216
Option 3: 2(27 + 12)
This option multiplies the common factor (6) by a different combination of numbers. However, it does not ensure that each group will have an equal number of blue and red jerseys since 27 and 12 are not factors of 24 and 30. Plugging in the values:
2(27 + 12) = 2(39) = 78
Therefore, the correct answer that shows how the coach should sort the jerseys using the GCF and the Distributive Property of multiplication over addition is 3(27+12).