During first semester, the ratio of the number of students in art class to the number of students in gym class was 2:7. However, the art classes were really small, and the gym classes were large, so the principal changed students’ classes for second semester. In second semester, the ratio of the number of students in art class to the number of students in gym class was 5:4. If 75 students were in art class second semester, how many were in art class and gym class first semester? *

Question

During first semester, the ratio of the number of students in art class to the number of students in gym class was 2:7. However, the art classes were really small, and the gym classes were large, so the principal changed students’ classes for second semester. In second semester, the ratio of the number of students in art class to the number of students in gym class was 5:4. If 75 students were in art class second semester, how many were in art class and gym class first semester? *

Answer 1

and what about shop classes?

Answer 2

Let's assume the number of students in art class and gym class during the first semester as "2x" and "7x" respectively, where "x" is a common factor.

According to the information given in the second semester, the ratio of the number of students in art class to the number of students in gym class was 5:4. Since there were 75 students in art class second semester, we can set up the following equation:

(5/4) * (7x) = 75

Multiplying both sides of the equation by (4/5), we get:

7x = 75 * (4/5)
7x = 60

Dividing both sides of the equation by 7, we get:

x = 60 / 7
x ≈ 8.57 (approx.)

Now, we can calculate the number of students in art class and gym class during the first semester:

Number of students in art class first semester = 2x
Number of students in art class first semester = 2 * 8.57
Number of students in art class first semester ≈ 17.14 (approx.)

Number of students in gym class first semester = 7x
Number of students in gym class first semester = 7 * 8.57
Number of students in gym class first semester ≈ 59.99 (approx.)

Since we can't have fractional students, we can round off the number of students in art class and gym class first semester:

Number of students in art class first semester ≈ 17
Number of students in gym class first semester ≈ 60

Therefore, there were approximately 17 students in art class and 60 students in gym class during the first semester.

Answer 3

To solve this problem, we need to set up a system of equations based on the given information.

Let's assume that in the first semester, the number of students in art class is 2x, and the number of students in gym class is 7x.

In the second semester, the number of students in art class is 5y, and the number of students in gym class is 4y. We also know that the number of students in art class in the second semester is 75.

So, we can set up the equation: 5y = 75

To solve for y, we divide both sides of the equation by 5:
y = 75/5 = 15

Now that we know y, we can substitute it back into the equation for the first semester to find the number of students in art class and gym class:

Number of students in art class in the first semester = 2x = 2 * 15 = 30
Number of students in gym class in the first semester = 7x = 7 * 15 = 105

Therefore, there were 30 students in art class and 105 students in gym class during the first semester.

Note: It is important to remember to set up equations based on the given information and solve for the unknown variables to find the answer to the question.

Answer 4

arts : gym = 2:7 = 2x : 7x

second semester:
arts : gym = 5y : 4y
5y = 75
y = 15
so in 2nd semester: 75 arts and 60 gym

assuming that there 135 students in both semesters, and students were
simply shuffled around, we have to split those 135 into a ratio of 2:7

2x + 7x = 135
9x = 135
x = 15

so in the first semester
2x = 30
7x = 105

Horrible decision by principal, as if there is no difference between
studying art and taking gym!