Question 1014611
here's what i think.


h = money hunter makes in a week.
n = money naomi makes in a week.
j = money jake makes in a week.


h + n + j <= 330


this means that the total that they all make in a week has to be less than or equal to 330.


you are given that hunter makes two times as much in a week as naomi.


the equation for this would be h = 2n.


you are given that naomi makes 30 more in a week than jake.


the equation for this is n = j + 30


you have 3 equations to work with.


h + n + j <= 330
h = 2n
n = j + 30


you want to convert everything in terms of one of the variables if that is possible.


since h = 2n and n = j + 30, then h = 2n becomes h = 2 * (j + 30) which becomes h = 2j + 60.


your equation are now:


h + n + j <= 330
h = 2j + 60
n = j + 30


in the first equation, you can replace n with j + 30 and you can replace h with 2j + 60 to get:


h + n + j <= 330 becomes (2j + 60) + (j + 30) + j <= 330.


remove parentheses to get 2j + 60 + j + 30 + j <= 330.


combine like terms to get 4j + 90 <= 330.


subtract 90 from both sides of this equation to get 4j <= 240.


divide both sides of this equation by 4 to get j <= 60.


since n = j + 30, then if j <= 60, n has to be <= 90


since h = 2j + 60, then if j <= 60, h has to be <= 180.


you get:


j <= 60
n <= 90
h <= 180


the maximum they can be is:


j = 60
n = 90
h = 180


the total of j + n + h would be 330.


this agrees with the problem statement so far.


the minimum they can be is calculated as follows:


the smallest one is j.


none of them can go negative.


the smallest j can be is 0.


the smallest n can be is 30 because n = j + 30.  
when j is equal to 0, n is equal to 30.
if n went below 30, j would be negative, which is  not allowed.


the smallest h can be is 60 because h = 2j + 60.
when j is equal to 0, h is equal to 60.
if h went below 60, j would be negative, which is not allowed.


hunters range is from 60 to 180 inclusive.
naomi's range is from 30 to 90 inclusive.
jake's range is from 0 to 60 inclusive.


in interval notation, you get:


h = [60,180]
n = [30,90]
j = [0,60]


based on this, the minimum they all can be is 90 total and the maximum they all can be is 330 total.