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Mr. Tan has some charity tickets. If he sends 4 tickets each to some companies, he will need 20 more. However, if he sends 3 each to the same companies,he will have a remainder of 50 tickets. How mant tickets does he have?

Posted in Math, asked by olive buenavista, 6 years ago. 2209 hits.

1

SOL ---    

Let the number of tickets Mr Tan has be X .   Let the number of companies be Y                                                                                        According to first condition ,  X + 20 = 4Y    (he sends 4 tickets each to Y companies . he will need 20 more )

According to second condition ,      X-50 =3Y ( he sends 3 tickets each to Y companies , 50 tickets remains with him )    

NOW lets rearrange these 2 equations and solve them simultaneously

                                 We get      X-4Y = -20         (1)

                                                 X-3Y = 50          (2)

Substacting equation 2 from equation 1 we get ,

                                                                   X-4Y=-20 

                                                                -

                                                                  X- 3Y = 50


                                                                 -   +      -

 


                                                             -4Y + 3Y = -20 - 50

                                                                  -Y     =   -70

                                                                    Y    =70                      ( 3 )

           Substituting the value of Y =70 in equation  1 we get the value of X .

                                           X- 4 * 70 =  -20 

                                           X - 280   = -20 

                                                 X     =  -20 + 280 

                                                 X     =    260

Answer - Mr Tan has 260 tickets and number of companies equals to 70 .

 

 

amit helekar
amit helekar - 6 years ago
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1

Let the number of tickets  he has be X

Let the number of companies be Y

If he sends 4 tickets each to some companies, he will need 20 more

so 4*Y=X+20

if he sends 3 each to the same companies,he will have a remainder of 50 tickets

3*Y=X-50

Thus we have two equations in two variables,

4*Y=X+20

3*Y=X-50

We want to find how many tickets does he have that means we want to find X,

So we have to eliminate Y from two equations.

From first equation,

Y=(X+20)/4

Substituting value of Yin second equation,

3*Y=X-50

3*(X+20)/4=X-50

3*(X+20)=4*(X-50)

3X+60=4X-200

4x-3x =200+60

X=260

So he has 260 tickets in his hand.

Number of companies is Y=(X+20)/4=260+20/4 = 280/4 = 70

when he give 4 tickets to 70 companies, he needs 280 tickets. but he has only 260 and so he needs 20 more.

when he gives 3 tickets to 70 companies, he only want 210 tickets and so he has 50 tickets more in his hand.

So the total number of tickets in his hand is 260 tickets.

vinu omanan
vinu omanan - 6 years ago
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