Math question on IXL?

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Two sisters have decided to watch all the episodes of a popular TV show on DVD. Megan has already watched 2 episodes and will continue to watch the show at a rate of 2 episodes per day. Sophia, who hasn't yet seen the show, will start watching 3 episodes per day. Once the two sisters get to the point where they have watched the same number of episodes, they plan to finish the series together. How long will that take? How many episodes will each sister have watched at that point?

In  days, the sisters will each have watched  episodes of the show.

Answer 1

Let's start by breaking the question down into two parts. First, let's look at Sophia's rate of show watching and translate it into a mathematical equation. Sophia will start watching the show at 3 episodes per day, so we could express the total amount of episodes watched by Sophia over any amount of days by the equation:

S = 3d

S = the amount of episodes watched by Sophia

d = the amount of days Sophia has spent watching episodes

Now we can do the same for Megan. Megan has already seen 2 episodes of the show, so no matter what our equation looks like, we will have to add 2 episodes to it to account for this. She watches at a rate of 2 episodes per day, so her equation will be:

M = 2d + 2

M = the amount of episodes watched by Megan

d = the amount of days Sophia has spent watching episodes at this rate

Now, we can go about finding how many days it will take for Megan and Sophia's watched episode count to be equal. At that point, S will equal M, so we can set both equations equal to each other and substitute in the equations we just came up with:

3d = 2d + 2

Let's use algebra to solve for d by isolating it. We can subtract 2d from both sides of the equation to get:

d = 2

Therefore, after 2 days, both Sophia and Megan will have watched the same amount of episodes. Additionally, we can plug the number 2 back into either Sophia or Megan's episode watching equation for "d", and we will then see that the total number of episodes that both Sophia and Megan watch after 2 days is 6 episodes each..