Question

Lucy wants to have a fun-filled day without spending too much money. The local zoo charges a $25 entry fee and a parking fee of $1 per hour. The local circus charges a $20 entry fee and a parking fee of $2 per hour.

Create a system of equations that Lucy could solve to determine which entertainment has the lower cost y, based on the number of hours, x, that she plans on staying.

Enter each equation on a separate line.

Answer 1

The required system of equations is,

`y=25+x`

`y=20+2x`.

Explanation:

Let the number of hours spent by Lucy = x

It is given that,

Local zoo charges initial fee $25 and per hour fee $1.

So, the equation representing the cost if Lucy stays 'x' hours is,

`y=25+x` in dollars.

Also, Local citcus charges initial fee $20 and per hour fee $2.

So, the equation representing the cost if Lucy stays 'x' hours is,

`y=20+2x` in dollars.

Since, the objective function for the situation is to 'minimize the cost'.

So, upon solving the equations, we will get the minimum value as,

25+x = 20+2x

i.e. x= 5

Thus,

`y=25+x` implies
`y=25+5` i.e. y= $30

`y=20+2x` implies
`y=20+2* 5` i.e.
`y=20+10` i.e. y= $30

Thus, the minimum value is $30.

The required system of equations is,

`y=25+x`

`y=20+2x`.