Answer:
a.) x + 2
b.)2 + x
12. Yes, the expressions x + 2 and 2 + x are equivalent.
13. No, I do not agree with Douglas's statement that soccer balls cost 2 4/5 times as much as baseballs.
To find out if soccer balls cost 2 4/5 times as much as baseballs, we can multiply the cost of a baseball by 2 4/5:
(2 4/5) * $5 = (14/5) * $5 = $14
As we can see, the result is equal to the cost of a soccer ball, which means soccer balls do not cost 2 4/5 times as much as baseballs. The cost of a soccer ball is equal to 2 times the cost of a baseball, not 2 4/5 times.
Step-by-step explanation:
a.) The algebraic expression that represents Dr. Grunion's purchase is:
x + 2
Step-by-step explanation:
In this expression, "x" represents the number of soccer balls purchased by Dr. Grunion, and "2" represents the number of baseballs purchased. By adding these two terms, we get the total number of items Dr. Grunion bought.
For example, if Dr. Grunion bought 3 soccer balls, the expression would be 3 + 2 = 5, indicating that he bought 5 items in total (3 soccer balls and 2 baseballs).
b.) The algebraic expression that represents Bill and Raj's purchase is:
2 + x
Step-by-step explanation:
In this expression, "2" represents the number of baseballs bought by both Bill and Raj, and "x" represents the number of pairs of sweat socks bought by each person. By adding these two terms, we get the total number of items each person bought.
For example, if each person bought 4 pairs of sweat socks, the expression would be 2 + 4 = 6, indicating that each person bought 6 items in total (1 baseball and 4 pairs of sweat socks).
Since the value of "x" is the same in both expressions (as stated in the question), it means that the number of pairs of sweat socks bought by Bill and Raj is equal to the number of soccer balls bought by Dr. Grunion.
12. Yes, the expressions x + 2 and 2 + x are equivalent.
Step-by-step explanation:
The expressions x + 2 and 2 + x are equivalent because addition is commutative. This means that changing the order of the terms being added does not change the result.
For example, if x = 3, then x + 2 = 3 + 2 = 5. Similarly, 2 + x = 2 + 3 = 5. Both expressions result in the same value, indicating that they are equivalent.
13. No, I do not agree with Douglas's statement that soccer balls cost 2 4/5 times as much as baseballs.
Step-by-step explanation:
To determine if soccer balls cost 2 4/5 times as much as baseballs, we need to compare the prices of soccer balls and baseballs.
Let's assume the cost of a soccer ball is $14 and the cost of a baseball is $5.
To find out if soccer balls cost 2 4/5 times as much as baseballs, we can multiply the cost of a baseball by 2 4/5:
(2 4/5) * $5 = (14/5) * $5 = $14
As we can see, the result is equal to the cost of a soccer ball, which means soccer balls do not cost 2 4/5 times as much as baseballs. The cost of a soccer ball is equal to 2 times the cost of a baseball, not 2 4/5 times.