Question

4. Max went to the amusement park one weekend. His all time favorite ride is the RockingMouse rollercoaster. He was interested in how many of each type of cart there was on the ride,some were small and held 2 people, and some were bigger and held 4 people. He asked andfound out there was a total of 15 carts and 40 people can ride at one time. How many of eachtype of cart is there on the rollercoaster?

Answer 1

Let's use the variable x to represent the number of small carts and y to represent the number of big carts.

Since the total number of carts is 15, we have the equation:

`x+y=15`

And if the total number of people that can ride at one time is 40, we have the equation:

`2x+4y=40`

From the first equation, let's isolate y and use its value in the second equation:

`\begin{gathered} x+y=15 \\ y=15-x \\ \\ 2x+4y=40 \\ 2x+4(15-x)=40 \\ 2x+60-4x=40 \\ -2x=40-60 \\ -2x=-20 \\ x=10 \\ \\ y=15-x \\ y=15-10 \\ y=5 \end{gathered}`

Therefore there are 10 small carts and 5 big carts.