At Central High School, the sophomore class has 60 more students than the freshman class. The junior class has 50 fewer than twice the number of students in the freshman class. The senior class is three times as large as the freshman class. If there are a total of 1,424 students at Central High School, how many students are in the freshman class?

Question

At Central High School, the sophomore class has 60 more students than the freshman class. The junior class has 50 fewer than twice the number of students in the freshman class. The senior class is three times as large as the freshman class. If there are a total of 1,424 students at Central High School, how many students are in the freshman class?

Answer 1

If the classes are a,b,c,d, then

b = a+60
c = 2a-50
d = 3a

a+b+c+d = 1424
a+(a+60)+(2a-50)+(3a) = 1424
7a + 10 = 1424
7a = 1414
a = 202

Answer 2

Use the “Uncle Sam Will Give You a Home In The Flathead Indian Reservation,” that describes land available in Montana, 1909 poster to answer the question.

What seeming contradictions is apparent in this poster? Explain
A. The poster targets Native Americans, trying to get them to buy land that they technically already owned.
B. The poster targets white settlers but encourages them to move onto land reserved for Native Americans.
C. The poster targets those wishing to escape the city but attempts to encourage the founding of new cities.
D. The poster targets those who want to make money out west without explaining the costs of mining tools.

Answer 3

B. The poster targets white settlers but encourages them to move onto land reserved for Native Americans. This is a contradiction as the land was reserved for Native Americans, but the poster is encouraging white settlers to move onto that land. It goes against the idea of reservation and instead promotes colonization.

Answer 4

To find the number of students in the freshman class, we need to set up equations based on the information given.

Let's denote:
F = number of students in the freshman class
S = number of students in the sophomore class
J = number of students in the junior class
R = number of students in the senior class

From the given information, we can write the following equations:

1) S = F + 60
2) J = 2F - 50
3) R = 3F

We also know that the total number of students is 1,424, so we can write another equation:

4) F + S + J + R = 1,424

Now we have a system of four equations. We can substitute the expressions for S, J, and R from equations 1, 2, and 3 into equation 4 to solve for F:

F + (F + 60) + (2F - 50) + (3F) = 1,424

Combining like terms:

7F + 10 = 1,424

Subtracting 10 from both sides:

7F = 1,414

Dividing by 7:

F = 202

Therefore, there are 202 students in the freshman class at Central High School.