Carrie and Kenny both play soccer. Kenny scored 3 times as many goals as Carrie. Together, they scored 12 goals. Could Carrie have scored 2 goals? Why or why not?
a. Yes, because 2 goals is less than the total number of goals scored
b. No, because 3(2) + 2 ≠ 12
c. Yes, because 2 goals is less than the number of goals Kenny scored
d. No, because 3(2) ≠ 12
b. No, because 3(2) + 2 ≠ 12.
If Carrie scored 2 goals, then Kenny would have scored 6 times as many goals, which is 12 goals. Together, they would have scored 14 goals, not 12. Therefore, it is not possible for Carrie to have scored 2 goals.
Katie and Mina both commute to work. Katie's commute on the train takes 10 minutes more than one half as many minutes as Mina's commute by car. It takes Katie 30 minutes to get to work. Write an equation to determine how many minutes it takes Mina to get to work.
a. 30 = one halfx + 10
b. 30 = one halfx − 10
c. 30 = 2x − 10
d. 30 = 2x + 10
a. 30 = one halfx + 10
Here's the reasoning:
Let's call the number of minutes it takes Mina to get to work "x".
According to the problem, "Katie's commute on the train takes 10 minutes more than one half as many minutes as Mina's commute by car."
Translated into an equation:
Katie's commute time = (1/2)x + 10
We also know that "It takes Katie 30 minutes to get to work."
So we can set up another equation:
Katie's commute time = 30
Putting these two equations together, we get:
(1/2)x + 10 = 30
Subtracting 10 from both sides:
(1/2)x = 20
Multiplying both sides by 2:
x = 40
Therefore, Mina's commute to work takes 40 minutes.
In science class, the average score on a lab report is 82 points, with all students scoring within 3.2 points of the average. If x represents a student's score, write an equation that represents the minimum and maximum scores.
a. |x − 3.2| = 82
b. |x + 3.2| = 82
c. |x − 82| = 3.2
d. |x + 82| = 3.2
c. |x − 82| = 3.2
Here's the reasoning:
The problem states that "the average score on a lab report is 82 points, with all students scoring within 3.2 points of the average." This means that any student's score (represented by x) must be somewhere between the minimum score and the maximum score:
minimum score = 82 - 3.2 = 78.8
maximum score = 82 + 3.2 = 85.2
So the equation that represents the minimum and maximum scores is:
|x - 82| = 3.2
This equation says that the absolute value of the difference between x and 82 is equal to 3.2, which means that x can be 3.2 points above or below 82.
The correct answer is: b. No, because 3(2) + 2 ≠ 12
Carrie could not have scored 2 goals because if Kenny scored 3 times as many goals as Carrie, then Carrie's goals should be a third of Kenny's goals. If we let 'x' represent the number of goals Carrie scored, then Kenny scored 3x goals. Together, they scored 12 goals, so we can write the equation as:
x + 3x = 12
Combining like terms, we get:
4x = 12
Dividing both sides by 4, we find:
x = 3
This means that Carrie scored 3 goals, and if Kenny scored 3 times as many goals, Kenny scored 9 goals. Therefore, 2 goals is not a possible number for Carrie's goals.
To determine if Carrie could have scored 2 goals, we need to examine the information given in the problem. It is stated that Kenny scored 3 times as many goals as Carrie, and together they scored 12 goals.
Let's suppose Carrie scored x goals. According to the information given, Kenny scored 3 times as many goals as Carrie, so Kenny scored 3x goals.
Since the total number of goals scored by both Carrie and Kenny is 12, we can write the equation:
x + 3x = 12
Combining like terms, we get:
4x = 12
Dividing both sides of the equation by 4, we find:
x = 3
So, Carrie scored 3 goals.
Therefore, Carrie could not have scored 2 goals, because the number of goals she scored is 3, not 2.
Thus, the correct answer is d. No, because 3(2) ≠ 12.