Systems of Equations Application Word Problems

Question

The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 210 people entered the park, and the admission fees collected totaled 590 dollars. How many children and how many adults were admitted?

Answer 1

As the title implies, we can set up a system of two equations for our two variables - the number of children (C) and adults (A) that entered the park. One equation will describe the number of people that entered the park, while the other will describe the amount of money collected:

C + A = 210

1.5C + 4A = 590

We can solve this several different ways. I will solve by rearranging the top equation for A, then substituting into the bottom equation.

A = 210 - C

1.5C + 4(210-C) = 590

1.5C + 840 - 4C = 590

-2.5C + 840 = 590

-2.5C = -250

C = -250/-2.5

C = 100 children

By substituting this value into our first equation, we can find the number of adults.

100 + A = 210

A = 110 adults

I hope this helped!