Question

The admission fee at an amusement park is $1.50 for children and four dollars for adults. On a certain day 265 people enter the park and the admission fees collected totaled $710 how many children and how many adults were admitted?

Answer 1

Number of children equals 140

Number of adults equals 125

Step-by-step explanation:

Let's call x the number of children in the park and y the number of adults.

If 265 enter the park, we can write the following equation:

x + y = 265

Additionally, they collect $1.50 per child and $4 per adult, and in total they collecter $710, so

1.50x + 4y = 710

Now, we need to solve the following system of equations

x + y = 265

1.5x + 4y = 710

Solving the first equation for y, we get:

x + y - x = 265 - x

y = 265 - x

Then, replacing y = 265 - x on the second equation, so

1.5x + 4y = 710

1.5x + 4(265 - x) = 710

1.5x + 4(265) - 4x = 710

-2.5x + 1060 = 710

Solve the equation for x

-2.5x + 1060 - 1060 = 710 - 1060

-2.5x = -350

-2.5x/(-2/5) = -350/(-2.5)

x = 140

Finally, we can calculate the value of y

y = 265 - x

y = 265 - 140

y = 125

Therefore, the number of children was 140 and the number of adults was 125.