Question

The admission fee at an amusement park is $2.75 for children and $5.00 for adults. On a certain day, 260 people entered the park, and the admission fees collected totaled $1030. How many children and how many adults were admitted?

Answer 1

On this day there 140 adults and 120 children were admitted to the amusement park.

Explanation:

If on a given day they had 260 people on the park then on that day the sum of children and adults must be equal to 260. We can write this in an equation form by calling children 'c' and adults 'a', as follows bellow:

a + c = 260

On this given day they collected a total of $1030, so the sum paid by children and adults must be equal to this value. In order to know how much was collected from children we must take the amount of them who visited the park on that day and multiply it by the fee, the same must be done to adults. So we have:

5*a + 2.75*c = 1030

Using the first equation we can isolate the variable for adults and determine a relation between the number of adults and children. We have:

a = 260 - c

We can use this expression on the second equation in order to solve for 'c'. We have:

5*(260 - c) + 2.75*c = 1030

1300 - 5*c + 2.75*c = 1030

-2.25*c = 1030 - 1300

-2.25*c = -270

2.25*c = 270

c = 270/2.25 = 120

So,

a = 260 - 120 = 140

On this day there were 140 adults and 120 children.