SOLUTION: A total of 1200 students attend a top high school. The ratio of teachers to students is 1:30. How many teachers are there at the school? Two-fifth of the students own personal

Hi, there--

THE PROBLEM:
a) A total of 1200 students attend a top high school.  The ratio of teachers to students is 1:30. 
How many teachers are there at the school?

b) Two-fifth of the students own personal computers.  How many students do not own Personal computers?  

c) Thirty percent of the students who own personal computer also own play stations. What 
fraction of the students in the school own play station?


A SOLUTION:
a) A total of 1200 students attend a top high school.  The ratio of teachers to students is 1:30. 
How many teachers are there at the school?

We can use the ratio of teachers to students to determine the the number of teachers in the 
school. There are several ways to set up a proportion, depending upon what you compare. 
Here is one way.

Let T be the number of teachers.
Let S be the number of students.

The most challenging part of these problems can be setting up a valid proportion. I like to
say the proportion aloud and listen for the matching pattern: 
"Teachers" is to "Students" as 1 is to 30

The proportion is T : S = 1 : 30 or .

We know that we have 1200 students so we substitute 1200 for S in the proportion.


Solve for T.

If the denominators on both sides of the equation are the same, it will be easy to see the 
value of T. Notice that 30*40=1200, so we multiply the right side of the proportion by 40/40.





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There are 30 teachers at the high school.
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b) Two-fifth of the students own personal computers.  How many students do not own 
Personal computers?  

We know that we have 1200 students. To solve the problem 2/5 of 1200, we multiply 
(2/5)*(1200).

Multiply 2*1200, then divide the result by 5.

2*1200 = 2400
2400/5 = 480

480 students own personal computers. We want to know how many students do NOT 
own PCs, so we subtract 1200-480=720.

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720 students do not own PCs.
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c) Thirty percent of the students who own personal computer also own play stations.  What 
fraction of the students in the school own play station?

We know that 480 students own personal computers. Since 30% of them also own play
stations, we want to find 30% of 480. 

When you multiply a percent, you need to convert it to the decimal equivalent. 30% means
30 out of 100 or 30 hundredths or 0.30. Now multiply 0.30 * 480.
0.30 * 480  = 144.

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144 students own a personal computer and a playstation.
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If you need multiplying decimals, here is a good link:
http://www.mathsisfun.com/multiplying-decimals.html

Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com