Question

All of the 6th grade students at West Village Middle School were asked if they would rather visit the Museum of Math or the Museum of Natural History.

75% of the students answered that they would rather visit the Museum of Mathematics, and the number of students who chose the Museum of Math was 30 more than the number of students who chose the Museum of Natural History.

How many 6th grade students are there at West Village Middle School?

Answer 1

To find the number of 6th grade students at West Village Middle School, we need to solve a system of linear equations using the given information.

Step-by-step explanation:

To solve this problem, let's assign variables to the unknown quantities. Let's say the number of students who chose the Museum of Math is x, and the number of students who chose the Museum of Natural History is y.

According to the problem, 75% of the students chose the Museum of Math. So we can write the equation: 0.75(x + y) = x.

We are also given that the number of students who chose the Museum of Math is 30 more than the number of students who chose the Museum of Natural History. So we can write the equation: x = y + 30.

We can solve this system of linear equations to find the values of x and y, which will represent the number of students. Once we find the solution, we can add the values of x and y to find the total number of 6th grade students at West Village Middle School.

Answer 2

Using the information given about the students' preferences for the two museums.

Then solving for the total number of students, will get 6th-grade students = x/0.75.

Step-by-step explanation:

To find the number of 6th-grade students at West Village Middle School, we can use the information given about the students' preferences for visiting the Museum of Math or the Museum of Natural History.

Let's assume the number of students who chose the Museum of Natural History is x.

According to the problem, 75% of the students chose the Museum of Math, which means 75% of the total number of students at the school.

We also know that the number of students who chose the Museum of Math is 30 more than the number of students who chose the Museum of Natural History. So, we can set up an equation:

• The number of students who chose the Museum of Math = 75% of the total number of students
• The number of students who chose the Museum of Natural History = x
• The number of students who chose the Museum of Math = x + 30

Setting up the equation: x + 30 = 75% of the total number of students

Rewriting 75% as a decimal: x + 30 = 0.75(total number of students)

Solving for the total number of students:

1. Subtract 30 from both sides: x = 0.75(total number of students) - 30
2. Divide both sides by 0.75: x/0.75 = total number of students

So, the total number of 6th-grade students at West Village Middle School is x/0.75.