Elementary Algebra

Question

The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 345 people entered the park, and the admission fees collected totaled 980 dollars. How many children and how many adults were admitted?

Answer 1

The admission fee at an amusement park is 1.5 dollars for children and 4 dollars for adults. On a certain day, 345 people entered the park, and the admission fees collected totaled 980 dollars. How many children and how many adults were admitted?

=>

no. of children = x

no. of adults = y

On a certain day, 345 people entered the park

x+y =345

y=345 - x

1.5 dollars for children and 4 dollars for adults and the admission fees collected totaled 980 dollars

1.5 x + 4y = 980

1.5x +4(345-x) =980

1.5 x + 1380 -4x =980

-2.5 x = -400

x = 160

y=345 - x = 345 -160 = 185

no. of children = x =160

no. of adults = y =185

Answer 2

These used to get me, too. Let's see what we can do.

Let a = the # of adult tix and c = the # of child tix.

c + a = 345

1.5c + 4a = 980

There's a couple of ways to solve this. I'm going to use substitution. First, solve the first equation for c or a. I'll do a.

a = 345 - c

Now, expressions or terms on either side of the = can be swapped out for each other, since they are EQUAL.

1.5c + 4(345 - c) = 980

1.5c + 1380 - 4c = 980

-2.5c = -400

c = 160

Hey, we have a value for c, which we swap into the first equation.

a = 345 - 160

a = 185

Hope this helps!

Answer 3

Hello Sophia,

I hope this short video helped you understand how I created the two important equations to solve this question. Feel free to contact me if you have any questions.

Thank you,

Beto N.