Question

A swimming pool charges $6 for adults and $4 for children. On a particular day, they made $1,326 in admissions. If a total of 289 people paid to swim, how many kids and how many adults

Answer 1

Children: 204

Adults: 85

Explanation:

Representation: let k represent the number of children and a the number of adults.

Equations: k + a = 289 (numbers of people)

($4/child)k + ($6/adult)a = $1,326

Let's solve this system of equations by substitution. Since k + a = 289, a = 289 - k. Substituting 289 - k for a above, we get this equation in one variable:

($4/child)k + ($6/adult)(289 - k), or, without units, 4k + 1734 - 6k = 1326.

The next step is to combine like terms: -2k = -408.

Dividing both sides by -2, we get k = 204. There are 204 children in the pool and 289 - 204 adults, or 85 adults.

Children: 204

Adults: 85

Answer 2

x= # of adults
y= # of children

1326= 6x + 4y
289= x + y

We are going to do substitution.

x = 289-y
1326= 6(289-y) + 4y
1326= 1734 -6y + 4y
1326= 1734 + -2y
-408= -2y
204 = y

Since we now have a value for y, we should plug that back into the equation we got the x value from to find the actual numerical value of x.

289= x + y
289= x + 204
85= x

In conclusion, 85 adults and 204 adults went to the swimming pool.