Something appears to be wrong with the phone question. I don't believe any of the answers. I still got it right by choosing the answer that was better than the others ... but I think it is a flawed question.
I think the only confusing part of it is the sentence
> The number of phones that she has left to fix at the end of each day can be estimated with the equation
"Has left to fix" could be misinterpreted as meaning "she has to fix this many," instead of simply "how many remain."
If you understand that it's just saying "P is how many remain", then it's clear that the formula is simply saying that she started with 108, and she fixes 23 per day.
"Where d is the number of days she has worked that week"
Substitute d = 0, meaning she has worked no days yet. Then P = 108. Thus when she has worked no days yet, she has 108 phones to repair. Alternately phrased, Kathy starts each week with 108 phones to fix.
> I don't believe any of the answers. … I think it is a flawed question.
Genuinely curious, not confrontational: why? That is, why do you think that the answer that is marked correct is not, or might not, actually be correct?
> For example, what if she was given 216 phones to fix per week, and she fixes 46 per day?
I'm sorry; I'm confused. In that case, the equation would say that there are P = 216 - 46d phones to fix after d days. This isn't the same equation as the given P = 108 - 23d, although its right-hand side is proportional to the right-hand side of the original.
(That is, I'd agree with you if we were given just the ratio (phones to fix per week)/(phones fixed per day), but we're given more than that. Perhaps it's important to notice that we are given an equation (left-hand side = right-hand side), not just a formula (right-hand side by itself).)
But the question never stated that 108 and 23 meant anything more than numbers you use in the formula. So, if she were given 216 phones per week, and she fixes 46 per day, then the formula would hold true.
So the question does not provide enough information to select the answer they have designated as correct.
(This is many days later and I no longer have the question in front of me, and I'm not willing to invest the time to find it. But this was my thinking when I posted this).
