There are three times as many people in the psychology class as in the art history class. there are 16 more people in the algebra class then the art history class The total enrollment of the three classes is 86. How many students are enrolled in each class?.
So I know my equation involves 3, 16 and 8 . So am I multiplying and also dividing as well as subtracting?
Oops I meant to say 86.
call the classes p,h,a. The clues are:
p = 3h
a = h+16
p+a+h = 86
now start eliminating values:
p = 3h, so
3h+a+h = 86
a = h+16, so
3h + h+16 + h = 86
5h+16 = 86
5h = 70
h = 14
so, there are
14 art history students
42 psychology students
30 algebra students
Yes, you will use both multiplication and subtraction to solve the problem. Let's break it down step-by-step.
Let's assume the number of people in the art history class is "x".
According to the first statement, there are three times as many people in the psychology class as in the art history class. So, the number of people in the psychology class is 3x.
According to the second statement, there are 16 more people in the algebra class than the art history class. So, the number of people in the algebra class is x + 16.
The total enrollment of the three classes is 86. So, we can write the equation as:
x + 3x + (x + 16) = 86
Now, you can solve for x:
5x + 16 = 86
5x = 70
x = 14
Now that you have found the value of x, you can substitute it back into the equations to find the number of people in each class:
Art History class: x = 14
Psychology class: 3x = 3 * 14 = 42
Algebra class: x + 16 = 14 + 16 = 30
Therefore, the art history class has 14 students, the psychology class has 42 students, and the algebra class has 30 students.
To solve this problem, let's start by assigning variables to represent the number of students in each class.
Let's say the number of students in the art history class is x.
Based on the given information, the number of students in the psychology class would be three times the number of students in the art history class, so it would be 3x.
And the number of students in the algebra class would be 16 more than the number in the art history class, so it would be x + 16.
Now, we can form an equation using the total enrollment of the three classes, which is given to be 86:
x + 3x + (x + 16) = 86
Simplifying the equation, we combine the like terms:
5x + 16 = 86
Next, we isolate the variable by subtracting 16 from both sides of the equation:
5x = 70
To solve for x, divide both sides by 5:
x = 14
Therefore, there are 14 students in the art history class.
Based on our earlier calculations, the psychology class has three times the number of students in the art history class, so it would have 3 * 14 = 42 students.
The algebra class has 16 more students than the art history class, so it would have 14 + 16 = 30 students.
In summary, there are 14 students in the art history class, 42 students in the psychology class, and 30 students in the algebra class.