A group of 78 people attended a ball game. There were five times as many children as adults in the group. Determine the number of adults and children in the group

Answer 1

To start, let's define the variables: x = # of children and y = # of adults

We know the total number of people is 78, so: x + y = 78

We know that there are five times as many children as adults, so: x = 5y

Now substitute x = 5y into the first equation, we get ---> 5y + y =78

Now simplify and solve the equation:

6y = 78

y = 78/6

y = 13 (this is the number of adults)

Now input y into the second equation to find the number of children:

x = 5*13

x = 65 (this is the number of children)

Check your answers with the first equation: x + y =78

65 + 13 = 78

78 = 78

All finished! You now have your answers

Answer 2

We know the total number of children and adults is 78, so we can start by writing that out as:

78 = children + adults

Since there are 5 times as many children as adults we know

children = 5*adults

If we substitute this back into the original equaltion we are left with:

78 = 5*adults + adults

Then, just solve for adults (I'm going to use the variable a for adults and c for children):

78 = 6*a

a = 78/6

a = 13

Lastly, we need to determine the number of children using children = 5*adults:

c = 5*a

c = 5*13

c = 65

To double check we can add the number of children and adults to ensure the total is 78:

c + a = 78

65 + 13 = 78

78 = 78