John delivers newspapers he makes $5 the first week and $2 are added to his pay each week he delivers papers. Which expression could be used to find out how much he would make in a given week, w, after the first week?

a) 2w+5
b) 2(w-2)+5
c) 2(w-1)+5
d) 5w-2

you know it's going to involve a +2w somewhere, because he gets $2 more each week.

So, that only leaves A as the logical choice, and it fits because he starts out with 5, and for each w gets 2 more.

To find out how much John would make in a given week, we need to take into account that $2 are added to his pay each week after the first week. So, we can start with the initial pay of $5 and add $2 for each additional week.

Let's break down the options provided to see which expression accurately represents this scenario:

a) 2w + 5: This option suggests that $2 is multiplied by the number of weeks, and then added to $5. However, this is not accurate since John only receives an additional $2 each week, not a multiple of $2.

b) 2(w-2) + 5: This option deducts 2 from the number of weeks and then multiplies the result by $2, and finally adds $5. Again, this is not accurate because there is no deduction involved in John's pay.

c) 2(w-1) + 5: This option subtracts 1 from the number of weeks, multiplies the result by $2, and adds $5. This seems to correctly represent the scenario, as John receives $2 for each additional week after the first week.

d) 5w - 2: This option multiplies $5 by the number of weeks and then subtracts $2. This does not follow the given scenario since John's pay does not increase by $5 each week.

Based on the analysis, the expression that accurately represents how much John would make in a given week, w, after the first week is c) 2(w-1) + 5.