SOLUTION: Hello. I am having trouble with the following question. Can you please help? 500 tickets were sold for a music concert. Adult tickets sold for $7.50 and children tickets sold

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Question 530934: Hello. I am having trouble with the following question. Can you please help?
500 tickets were sold for a music concert. Adult tickets sold for $7.50 and children tickets sold for $4. Total ticket sales were $3312.50. How many of each kind of ticket were sold?
Found 2 solutions by oberobic, KMST:
Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website!
a = number of adult tickets sold
c = number of children ticks sold
a + c = 500 (given)
so
a = 500-c
.
7.5a = value of the adult tickets sold
4c = value of the children tickets sold
7.5a + 4c = 3312.5
.
substitute a = 500-c
.
7.5(500-c) + 4c = 3312.5
.
multiply by 10 to eliminate decimals
.
75(500-c) + 40c = 33125
.
37500 -75c + 40c = 33125
.
-35c = -4375
.
c = 125 child tickets
.
a = 500-c
a = 375 adult tickets
.
Check the value to make sure this is the right answer.
4*125 = 500
7.5*375 = 2812.5
500+2812.5 = 3312.5
Correct.
.
Answer: 375 adult tickets and 125 child tickets.
.
Done.

Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website!
Let a be the number of adult tickets sold.
Let c be the number of children sold.
Would you agree that a+c=500?
Would you agree that the total amount of money received for the children's ticket was 4c?
And that the total collected for adult tickets was 7.5a?
And that 7.5a+4c=3312.5?
That gives you a systen of two linear equations with two variables, and that is probably what you are studying in school. If you are studying that, you should have lern about "methods" to solve those systems of equations, like the substitution method and the elimination method.
Since a+c=500 looks really simple you could use it to find the expression for c that you could substitute in the other equation.
Or you could multiply that equation by (-4) and add it to the other equation.
Either way would lead you to 3.5a=1312.5 and a=375.
And with that and a+c=500 you would find that c=125.
There are other ways to solve it, too.