SOLUTION: There are 75 students in a classes A and B altogether. There are 61 students in classes A and C altogether. The ratio of the number of students in Class B to Class C is 5:3. How ma

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: There are 75 students in a classes A and B altogether. There are 61 students in classes A and C altogether. The ratio of the number of students in Class B to Class C is 5:3. How ma      Log On


   

Question 1179674: There are 75 students in a classes A and B altogether. There are 61 students in classes A and C altogether. The ratio of the number of students in Class B to Class C is 5:3. How many students are there in Class A?
Found 2 solutions by mananth, greenestamps:
Answer by mananth(16946) About Me  (Show Source):
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There are 75 students in a classes A and B altogether. There are 61 students in classes A and C altogether. The ratio of the number of students in Class B to Class C is 5:3. How many students are there in Class A?
A+B=75---------------------------1
A+C =61--------------------------2
B/C = 5/3
3B=5C
C=3B/5
SUBSTITUTE C IN (2)
A+3B/5 =61
5A+3B =305-----------------------(3)
1.00 A + 1.00 B = 75.00


5.00 A + 3.00 B = 305.00 .............2
Eliminate B
multiply (1)by -3.00
Multiply (2) by 1.00
-3.00 A -3.00 B = -225.00
5.00 A 3.00 B = 305.00
Add the two equations
2.00 A = 80.00
/ 2.00
A = 40.00
plug value of A in (1)
1.00 A + 1.00 B = 75.00
40.00 + 1.00 B = 75.00
1.00 B = 35.00
B = 35.00
Ans A = 40
B = 35




Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Yet another example of how to make a relatively easy problem difficult....

And it's still a mystery why that tutor consistently represents whole number quantities using 2 decimal places....

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Nearly always -- if not always -- the easiest way to start on a problem where a ratio like 5:3 is given is to call those two quantities 5x and 3x.

5x = # students in class B
3x = # students in class C

We can just let a represent the number of students in class A. Then the given information is

a+5x = 75
a+3x = 61

That immediately gives us

2x=14
x=7

Then

# students in class B = 5x = 35
# students in class C = 3x = 21

And finally

# students in class A = 75-35 = 40

or

# students in class A = 61-21 = 40