Amelia wants to have an A (90 or higher) in math this semester. Her test grades so far are 85, 95, 93, 88, and 97. What is the lowest grade she can make on the last test to keep an A?

*Solution to yesterday’s problem:*

The shortest paths from A to B are the ones that go exactly four units right and two units up, with no down or left movements. So we can think of it as four steps right with two up-steps in between them. To find the number of paths, we just look at how many different ways we can place the two up-steps.

First, say the first step was up. Then the second up-step could go after the first, second, third, fourth, or fifth step. That’s *5* possibilities. If the first up-step was the second one, the other up-step could go after the second, third, fourth, or fifth step. (It could not go before the first up-step because we have already covered this situation.) So that’s *4* possibilities. See the pattern? We can quickly complete the problem by adding 5 + 4 + 3 + 2 + 1 = *15 different paths.*

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