Algebra II Nostalgia

Yosuke's summer Algebra II class is nostalgic; it reminds me of when I took Algebra II over the summer. It was the summer before my freshman year at high school. I took it over three weeks at Duke University through the TiP program. At the time, it felt helplessly over my head. I honestly believed that I had reached my "math limit" and was incapable of learning the material. In the end, though, I managed to grasp the concepts, and I even scored 97 on the EOC.

Now I see myself in Yosuke, who was able to yawn his way through his regular math classes. He's struggling with Algebra II, and I can even sense a bit of hopelessness in him. I'm glad I'm here to help him, though, so he doesn't have to struggle by himself.

...
Well, he has to struggle by himself a little. We spent a long time working on this problem, and he's close to figuring it out. I left before we finished, asking him to try and complete it on his own.

Here is the problem:
1. You scored 92 and 90 on the first two tests. There is one more test. What range of grades should you get on the third test for your average to be between 88 and 93?
2. Repeat #1, only this time the third test counts twice as much as the other tests.

Yosuke worked out #1 with a bit of help from me. I recognized that the second problem is more difficult, but I didn't think he would have as much trouble with it as he did. I gave him several hints, but finally I just had to leave him to work it out on his own. I want to help him, but I can't just tell him the answer, so I had to leave him struggling and feeling helpless. This is going to be a rough summer for both of us!