The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 283 people entered the park, and the admission fees collected totaled 862 dollars

Question

The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 283 people entered the park, and the admission fees collected totaled 862 dollars. How many children and how many adults were admitted?

Answer 1

This is a systems of equations problem!

Let's first set up our system by assigning x and y to mean something. Let x = number of children and y = number of adults.

First equation: Children cost $1.50 and Adults cost $4.00. In order to find the amount of money a group of children will cost, we multiply the number of children, x, by 1.5. This is represented by 1.5x. For adults, who cost 4 dollars to enter, we will use 4y. The total amount of money made on the given day was $862. To get this amount, we must add 1.5x and 4y.

1.5x + 4y = 862 works for the money equation involved.

Second equation: Total amount of people on the given day is 283. To get this number, we must add together x and y, or the number of children and adults.

x + y = 283

System of equations:

1.5x + 4y = 862

x + y = 283

Let's use substitution of the x variable to solve the system.

x + y = 283 <--- subtract x from both sides

y = 283 - x

Substitute y = 283 - x into the first equation.

1.5x + 4 (283 - x) = 862 <--- distribute 4 to 283 and -x

1.5x + 1132 - 4x = 862 <--- combine 1.5x and -4x

1132 - 2.5x = 862 <--- subtract 1132 from both sides

-2.5x = -270 <--- divide both sides by -2.5

x = 108

Substitute x =108 back into y = 283 - x

y = 283 - 108 = 175

There were 108 children and 175 adults.