Question

You are going to the giant wheel and need to figure out which deal is better. You can pay $\$32$ to go on the ride as much as you want, or you can pay $\$13$ to get in, plus an additional $\$1$ per ride, such that the total cost ($y$) is related to the number of rides $\left(x\right)$ by the equation, $x+13=y$.
If you go on a certain number of rides, the two options are equal in the terms of cost. How many rides is that? What is the cost?
Number of rides $\left(x\right)=$____, Cost $\left(y\right)=$ _____

Answer 1

We have two options.
The first option is to pay $\$32$ and go on rides as much as we want.
The total cost, $y=\$32$

For the second option, let the number of rides be $x$ and the total cost be $y.$

If you choose to pay $\$13$ to get it and pay additional $\$1$ per ride.
Then the cost of the additional rides $=\$1\times \left(x\right)$
$=\$x$
The cost of getting in $=\$13$
The total cost $=\$13+x$
$y=13+x$ ...eq (1) [given]

Now after certain rides, both the options are equal in terms of cost,
So, the total cost $=\$32$ [consider the first option]
$y=32$ ...eq (2)
Substituting the value of $y$ from equation (2) in equation (1), we get:
$\Rightarrow 32=13+x$
$\Rightarrow x+13=32$
$\Rightarrow x=32-13$
$\Rightarrow x=19$
Number of rides $=19$
Cost $=\$32$

$\Rightarrow$ Option D is correct.