Please help before I pull all my hair out!

[littlemissstrange]

Ok I have been working on this problem for hours now and they keep saying that I have the wrong answer. I'm gonna go loony soon.

The principal asked Mr. Green how many students there were in his math class. "Well", Mr. Green said, "3/4 of them are less than 16 years old , 2/3 are less than 15 years old, 12 are not yet 14 years old, and there are twice as many between the ages of 14 and 15 as there are between the ages of 15 and 16". How many students were in the class?


I don't need anything but how you got the solution, I want to know that, and a number of students. Thank you SO much!

 

[stapel]

Multi-post.

Pick a variable -- say, "x" -- to stand for the total number of students.

Write an expression, in terms of this variable, for the number that are under sixteen years old. What then is the expression for the number that are sixteen or older?

Write another expression, in terms of the vatriable, for the number that are under fifteen years old. From this and the first expression, you can get an expression for the number of students that are fifteen years old, since (under sixteen) minus (under fifteen) equals (between fifteen and sixteen).

You are given the absolute value of the number of students under fourteen. The number of students between fourteen and fifteen (that is, aged fourteen years and however many days) is the difference between "under fifeen years" and "under fourteen years", so do that subtraction.

You should now have one expression for "between fifteen and sixteen" and another expression for "between fourteen and fifteen". Plug those expressions into the relationship "(twice)(between 14 and 15) is (between 15 and 16)". Solve.

If you get stuck, please reply showing how far you have gotten in following these instructions. Thank you.

Eliz.

 

[soroban]

Hello, littlemissstrange!

This is a unique problem ... never seen one like it.
I found a solution ... maybe someone can find a simpler way.

The principal asked Mr. Green how many students there were in his math class.
"Well", Mr. Green said, "3/4 of them are less than 16 years old,
2/3 are less than 15 years old,
12 are not yet 14 years old,
and there are twice as many between the ages of 14 and 15 as there are between the ages of 15 and 16".
How many students were in the class?

Let N = number of students in the class.
Let x = number of students between 15 and 16.
Then 2x = number of students between 14 and 15.

The distribution looks like this:

. . --------------------- N ------------
. .---------- (3/4)N ------ . . . . . . .|
. .--- (2/3)N ----- . . . . .| . . . . . . |
. . . . . . . . . . . . | . . . . .| . . . . . . |
. . . .12 .|. .2x . | . .x. . | . . . . . . |
. . -------+-------+-------+---------+
. . . . . . 14 . . . 15 . . . 16

We have: . (3/4)N .= .3x + 12 . . ---> . . N .= .4x + 16

. . . . and: . (2/3)N .= .2x + 12 . . ---> . . N .= .3x + 18

Equating these two: . 4x + 16 .= .3x + 18 . . ---> . . x = 2

Hence, the youngest three groups have: .12, 4, 2 students
. . These 18 students comprise 3/4 of the class.

Therefore, the entire class has 24 students.

 

[Denis]

n = number of students

< 16 = 3n/4

< 15 = 2n/3 : so age "15" = 3n/4 - 2n/3 = n/12

<14 = 12 ; so :
2n/3 - 12 = 2(n/12)
2n/3 - 12 = n/6
4n - 72 = n
3n = 72
n = 24

 

[littlemissstrange]

n = number of students

< 16 = 3n/4

< 15 = 2n/3 : so age "15" = 3n/4 - 2n/3 = n/12

<14 = 12 ; so :
2n/3 - 12 = 2(n/12)
2n/3 - 12 = n/6
4n - 72 = n
3n = 72
n = 24

YAY!!!!!!!! It makes sense! You don't even understand how awesome you guys are! THANKIES!!