Question

The admission fee at an amusement park is $4.25 for children and $7.00 for adults. On a certain day, 378 people entered the park, and the admission fees collected totaled $2129. How many children and how many adults were admitted?

Answer 1

There are 188 kids and 190 adults

Explanation:

We can use systems of equations to determin how many kids and adults there are.

First we have to write this as an equation systems.

Let x be the amount of kids and y be the amount of adults.

`y=` the amount adults
`x=` the amount of kids

So from this we can get:

`x+y = 378`

"The amount of kids plus the amount of adults is equal to 378"

Now we have to make another term.

"The amount of kids times 4.25 is the total amount of money that the kids did cost at that day. The amount of adults times 7 is the total amount of money made on adults. The amount of money on that the kids costs plus the amount of money that the adults costs is equal to 2129 dollars"

`4.25x+7y=2129`

Now we have two systems:

`4.25x+7y=2129`
`x+y=378`

Im going to use the substitution method for this system so we get:

`x+y=378 => x=378 color(green)(-y)`

Put that into the other system:

`4.25x+7y=2129 => 4.25 color(green)((378-y))+7y=2129`

Now simplify:

`(4.25xx378)+(4.25xx-y)+7y=2129`

`1606.5-4.25y+7y=2129`

`1606.5+2,75y=2129`

`2.75y=522.5`

`y=(522,5)/(2,75)=190`

Now we know the amount of adults or what y is equal to. Now put that into any system you want.

`190+x=378`
`x=188`

And now we know there are 188 kids.

Chek your work by putting these numbers into a system:

`4.25x+7y=2129 =>4.25 color(green)((188)) + 7 color(green)((190))=2129`

Simplify:

`4.25 color(green)((188)) + 7 color(green)((190))=2129`

`799+1330= 2129`

`2129=2129 color(green) sqrt`

It was a long explanation but I feel it was needed.

Hope this helps!