Working out how many adults and children were in the party

Question

The entry prices at a theme park are adults 20 dlrs and children 15 dlrs. A group visited and were charged 105 dlrs. How many adults and children were in the party? There was at least one adult.

Answer 1

Here's another way to look at the problem.

adults 20 dirs

children 15 dirs

20+15=35

105/35=3

3 adults and 3 children

If the total cost was 120, then 120/35=3 R15.

3 adults, 3 children plus another child for a total of 3 adults and 4 children

If the total cost was 145, then 145/35=3 R40

3 adults, 3 children plus 2 more adults for a total of 5 adults and 3 children

It gets complicated when the cost gets higher and higher such as 160 dirs whereby you have 2 possible solutions. Give it a try.

Using 2 variables forces trial and error just like a large enough increase in price.

Answer 2

20a +15c = 105

divide by 5

4a +3c =21

a>0

3 adults and 3 childfen

4x3+3x3= 21

20x3 + 15x3 = 105

any positive integer number of adults larger than 0 gives a fractional number of children

except 3 adults, and 3 children

6 total in the group

a c

1 17/3=5 2/3

2 13/3= 4 1/3

3 9/3= 3

4 5/3= 1 2/3

5 1/3