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?. I need a little help on how to work this.
First, write the clues in math symbols:
p = 3h
a = h+16
a+h+p = 86
Now just start substituting to get rid of all the letters but one, then go back and calculate the other two values.
To solve this problem, let's break it down step by step:
Step 1: Assign variables
Let's call the number of students in the art history class "A". We are told that there are three times as many students in the psychology class as in the art history class, so we can call the number of students in the psychology class "3A". Additionally, we are told that there are 16 more students in the algebra class than in the art history class, so we can call the number of students in the algebra class "A+16".
Step 2: Write equations
We know that the total enrollment of the three classes is 86. So, we can write the equation:
A + 3A + (A+16) = 86
Step 3: Solve the equation
Combine like terms:
5A + 16 = 86
Subtract 16 from both sides of the equation:
5A = 70
Divide both sides of the equation by 5:
A = 14
Step 4: Calculate the number of students in each class
Now that we know the value of A, we can substitute it back into the equations to find the number of students in each class:
Number of students in the art history class (A) = 14
Number of students in the psychology class (3A) = 3 * 14 = 42
Number of students in the algebra class (A + 16) = 14 + 16 = 30
So, there are 14 students in the art history class, 42 students in the psychology class, and 30 students in the algebra class.