SOLUTION: 1250 persons went to see a circus-show. Each adult paid ₹75 and each child paid ₹25 for the admission ticket. Find the number of adults and number of children, if the t

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Question 1114004: 1250 persons went to see a circus-show. Each adult paid ₹75 and each child paid ₹25 for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to ₹61,250
Please hlep me.... i want the woking of ever step please....
Found 4 solutions by rothauserc, greenestamps, MathTherapy, ikleyn:
Answer by rothauserc(4718)   (Show Source): You can put this solution on YOUR website!
let a be the number of adults and c be the number of children
:
1) a + c = 1250
:
2) 75a + 25c = 61250
:
solve equation 1 for a
:
a = 1250 - c
:
substitute for a in equation 2
:
75(1250-c) +25c = 61250
:
93750 -75c +25c = 61250
:
-50c = -32500
:
c = 650
:
a = 1250 - 650 = 600
:
*****************************************************
number of adults is 600 and number of children is 650
:
check the answer with equation 2
:
75(600) + 25(650) = 61250
:
45000 + 16250 = 61250
:
61250 = 61250
:
answer checks
*****************************************************
:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The solution by the other tutor using substitution is fine....

However, when the two equations we start with are both of the form , I think a solution using elimination is easier than a solution using substitution.

(1) total number of people is 1250
(2) total cost is 61,250

Multiply equation (1) by 25 and subtract from equation (2):
(3)
(4)


The number of adults is 600; so the number of children is 1250-600=650.

Of course both methods are valid. Try both and find out which you like better.
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
1250 persons went to see a circus-show. Each adult paid ₹75 and each child paid ₹25 for the admission ticket. Find the number of adults and number of children, if the total collection from them amounts to ₹61,250
Please hlep me.... i want the woking of ever step please....
With the number of adults being A, and children, C, we get: A + C = 1,250 ------- eq (i)

                                                          75A + 25C = 61,250 ---- eq (ii)

The easiest approach is to DIVIDE eq (ii) by its GCF, which is 25. This gives you:

3A + C = 2,450 ------ eq (ii)

Now, SUBTRACT eq (i) from the MODIFIED form of eq (ii) to ELIMINATE C and get: 2A = 1,200

A, or number of adults = 

600 + C = 1,250 ------- Substituting 600 for A in eq (i)

C, or number of children =  

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
 .

It is a standard ticket problem.





Since you want to learn on how to solve such problems from the beginning to the end, I recommend you to read the lessons



    - Using systems of equations to solve problems on tickets 



    - Three methods for solving standard (typical) problems on tickets



in this site.





From these lessons, learn  on how to solve such problems once for all.





Also,  you have this free of charge online textbook in ALGEBRA-I in this site



    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.





The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".





 

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