first, read the problem and circle/underline any important information. it usually helps you sort it out.
so, the book has 288 pages total. she's read 90 out of 288. she wants to read 20 pages from here on out to finish the book. write an equation yourself before you worry about part A with her incorrect equation.
"90" here is going to be your constant number, because regardless of how much she reads every day from now on, she has already done 90. you add 90 and the 20 per day because they have to add up to 288 to show that she completed the book. the equation you should have is:
90 + 20d = 288
so this will help you answer part A and part B of the question. what did she get wrong? well, you can see that she did SOMETHING to get that big ol' 378 instead of 288. she probably added 90 instead of subtracting it; do some mental math or check it on a calculator, and, yep, that's definitely her mistake there. then, it looks like she also thought she needed to "subtract" 20 pages per day. that would mean... she read 20 less pages a day, rather than 20 more. and you can't unread something, so that's her second mistake.
to summarize for part A: she added 90 instead of subtracting it, then she's subtracting 20 pages a day rather than adding it to her completed work.
to find out how many pages she'll need to read a day, you just need to get "d" alone in the equation we wrote.
90 + 20d = 288 ... subtract 90
20d = 198 ... divide by 20
d = 9.9, but as the instructions state, "part of a day" is a full day. that means she'll need 10 days to complete her reading.
"show that your answer is reasonable." -- to be honest, i don't really know what they're asking for here. of course it's reasonable? we just solved it with logical math............... maybe they want you to plug the answer in? in that case, just check it real quick:
90 + 20d = 288
90 + 20(10)
90 + 200
290... 288. she would have time to 290 pages but she only has to take care of 288, so she'll finished it ??
