There Are 12 More Students Taking History Than Math. There Are Twice As Many Students Taking Psychology As There Are Students Taking Math. There Are 452 Students Enrolled In These Three Subject. Assume Each Student Is Taking Only One Of These Three Courses. How Many Are Taking History? How May Are Taking Math?
what have they told you?
h = m+12
p = 2m
h+m+p = 452
Now solve. Substitution is probably easiest.
86
To solve this problem, let's break it down step by step:
Step 1: Assign variables
Let's assign variables to the unknown quantities. Let's represent the number of students taking Math as "x". Since there are 12 more students taking History than Math, we can represent the number of students taking History as "x + 12". Finally, since there are twice as many students taking Psychology as there are taking Math, we can represent the number of students taking Psychology as "2x".
Step 2: Write the equation
The total number of students enrolled in these three subjects is 452. So, the equation becomes: x + (x + 12) + 2x = 452.
Step 3: Simplify the equation
Combine like terms: 4x + 12 = 452.
Step 4: Solve for x
Subtract 12 from both sides of the equation: 4x = 440.
Divide both sides by 4: x = 110.
Step 5: Calculate the number of students for each subject
Since x represents the number of students taking Math, there are 110 students taking Math. The number of students taking History is 110 + 12 = 122. The number of students taking Psychology is 2 * 110 = 220.
Therefore, there are 122 students taking History and 110 students taking Math.