Average example in Achievable content

Good morning I have a question on the average chapter in the course. Specifically on the 62 average that resulted from the math that we did. We balanced the equation 6x (+90) = 7x +28 and found that x = 62. This bothers me because in the lower right average pie in the average slice we used x+4 to denote the unknown number. This is the box that I want to use for her new average and when we put our (x = 62) in that slice it becomes 62+4 which is 66. I lost how we balance the top half of both pies and call that our average when the average in the ‘average pie’ lives in the bottom right slice and we are able to plug in the value we received for x. Thanks for reading and please help so I can move on with my life lol.

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From our chapter on Average problems on the GRE:

Samantha has taken 6 algebra tests this semester. If she gets a 90 on her next test, it will raise her average (arithmetic mean) by 4 points. What is her average now?

When we draw our circles, the x variable represents the current average. We don’t know it yet, but we can set the equations from the problem. Here are the steps more concisely:

  1. They’ve taken 6 tests so far, with an average of x per test, so that’s 6 * x points total right now
  2. After the next test, that’s 7 total tests, and the average raises to x+4, so that’s 7 * (x + 4) = 7x + 28 points total later
  3. To get from now to later, they took that one extra test and got 90 points. So now we can make the equation 6x + 90 = 7x + 28

Does that help clear it up?

Thanks for the quick response Justin. I had an instructor in grad school that told me ‘convince yourself’ about a topic I was resistant to. This is one of those times lol. I want to understand it more but I will move on knowing that someone can verify is correctness lol. I still want to plug in x in the lower right corner to get the averages box filled with a real number but having discussed this in detail understand the equation and when to stop when finding the new average. Thanks again, this was very helpful!

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