Answer:
100 Adults and 164 Children
Step-by-step explanation:
To solve this we will need to write two equations to solve for the two unknowns. Firstly, we know that tickets are 20 for children and 35 for adults, and that the total price was 6780. We can write an expression to represent this. 6780 is the total price, this also means it is the price of all the adults + the price of all the children. The total price of the adults tickets is the price of each ticket multiplied by the number of adults, so the total price of adult tickets can be represented by: 35A, 35 being the ticket price per adult, and A being the number of adults. Similarly the total children's price can be expressed as such: 20C, 20 being the price per child, and C being the number of children. Since we know that these two values total to 6780, we can now form an equation:
35A (total adult price) + 20C (total children price) = 6780
35A+20C=6780
Now we need another expression so we can substitute for one of the values. The other piece of information we are given, is that a total of 264 people entered the park. This means that the total number of adults + the total number of children = 264. Since we already have variables for the numbers of adults and children we now have our second equation:
A (number of adults) + C (number of children) = 264
A+C=264
Now we can use this second equation to substitute for one of the values in the first equation. Let's substitute for children:
If we rearrange the second expression we will get:
A+C-A=264-A
C=264-A
So now we substitute this expression into our first formula:
35A+20C=6780
C=264-A
35A+20(264-A)=6780
Now since we only have one unknown, we can simplify, expand and solve!
35A+20*264-20*A=6780
35A+5280-20A=6780
35A-20A+5280-5280=6780-5280
15A=1500
15A/15=1500/15
A= 100
A total of 100 adults were admitted.
Now we can use the number of adults to find the number of children using our second formula:
C=264-A
C=264-100
C=164
And there we are! A total of 100 adults and 164 children were admitted.
Hope this helped!
