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:
- They’ve taken 6 tests so far, with an average of x per test, so that’s 6 * x points total right now
- 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
- 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?