Answer:
60 Adults and 55 Children
Step-by-step explanation:
We can work this out by writing two equations for the two unknowns and substituting in one for the other.
The two unknown variables we have here are the number of children and the number of adults. We can represent these unknown variables with the letters A (adults) and C (children).
If 115 people attended the concert, it means that:
A (no. adults) + C (no. children) = 115
So our first equation is A+C=115
If the total receipts was $260, it means that the total adult prices + total children prices = 260.
The total adult prices = the cost of each adult ticket (2.5) multiplied by the number of adults that attended. This means that the total number of adult receipts can be represented as: 2.5A
Similarly the total children receipts = the cost per child multiplied by the number of children, so the total children receipts can be represented as: 2C.
Since all receipts added up to 260, our second equation is:
2.5A + 2C = 260
Now we have our two equations, let's substitute one in for the other:
A + C = 115
If we rearrange the equation by subtracting C from both sides, we see that the number of adults is = 115 - C. (A=115-C)
This means we can substitute '115-C' for A in the other equation:
2.5(115-C) + 2C = 260
This is so we only have one unknown in our equation so we can solve for it.
Now we can just expand the brackets and solve!
287.5 - 2.5C + 2C = 260
287.5 - 0.5C = 260
Add C to both sides so it is positive (not necessary but helps keep more tidy and avoid sign errors), and subtract 260 from both sides:
287.5 - 0.5C + 0.5C - 260 = 260 - 260 + 0.5C
27.5 = 0.5C
27.5/0.5=0.5C/0.5
C = 55
There were 55 children!
Now we can just minus 55 from 115 to find the number of adults (our first equation) as there was a total of 115 people.
115 - 55 = 60
60 Adults and 55 Children went to the concert.
Hope this helped!
