Final answer:
By setting up equations based on the given percentages and differences in the number of students preferring each museum, we can deduce that there are 60 6th grade students at West Village Middle School.
Step-by-step explanation:
To find out the total number of 6th grade students at West Village Middle School based on the information provided, we can set up an equation. Let x be the number of students who preferred the Museum of Natural History. Thus, the number of students who preferred the Museum of Mathematics would be x + 30, since it is given as 30 more than the number who chose the Museum of Natural History.
Since 75% of the students chose the Museum of Mathematics, we can express this percentage as a fraction of the total number of students, which we will call T. So, we have 0.75T = x + 30. We also know that all students chose one museum or the other, so the total number of students is the sum of the students who chose each museum: T = x + (x + 30).
By solving these two equations, we get:
- 0.75T = x + 30
- T = 2x + 30
From equation (2), we can substitute 2x for T in the first equation:
0.75(2x + 30) = x + 30
This simplifies to:
1.5x + 22.5 = x + 30.
Subtract x from both sides:
0.5x + 22.5 = 30.
Subtract 22.5 from both sides:
0.5x = 7.5.
Finally, divide both sides by 0.5 to find x:
x = 15.
Now that we have the number of students who preferred the Museum of Natural History, we can find the total number of students by plugging x into equation (2):
T = 2(15) + 30
T = 30 + 30
T = 60.
Therefore, there are 60 6th grade students at West Village Middle School.