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The cost of tickets for a play is $3.00 for adults and $2.00 for children. 350 tickets in total were sold between the adult and children tickets and $950 was collected. How many adult tickets (a) and children tickets (c) were sold?

 Apr 4, 2020
 #1
avatar+178 
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Let's suppose the number of adult tickets sold are x, and the number of child tickets sold is y. 

If 350 tickets were sold, we can say that for our first equation, x + y = 350. 

Since $950 was collected, we can say that our second equation will be 3x + 2y = 950.

Here are our two equations: x + y = 350

                                             and

                                             3x + 2y = 950.

 

Since x + y = 350, we know that x = 350 - y.

Plugging this into the second equation, we will get 3 ( 350 - y ) + 2y = 950.

Expanding, we get 1050 - 3y + 2y = 950.

We can then combine the ys together, to get 1050 - y = 950. 

Subracting 1050 from each side, we'll get -y = -100.

Finally, flip the negative signs into positive signs, and we'll get y = 100, which means that the number of child tickets sold is 100.

 

All you have to do now is plug the number of child tickets into the first equation, solve, and then you will get the number of adult tickets sold. 

 

I hope this helps, good luck. 

 Apr 4, 2020
 #2
avatar+23699 
+1

a = adult tix              value =    $3 a

c = child tix =  350-a      value = $ 2 (350-a)      summed = $ 950

 

3a     +       2(350-a)      =    950       solve for 'a' , the number of adult tix, then  350 - a = child tix

 Apr 4, 2020

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