Question 677031
We need to name/define variables:
{{{y}}} = number of cups of hot chocolate consumed in a day in Fairbanks.
{{{x}}} = temperature in degrees Celsius
 
"For each rise of 1 degrees celsius, their consumption decreases by 30 cups per day."
That tells you that {{{y}}} is a linear function of {{{x}}}, so we should be able to write it as 
{{{y=mx+b}}} with some constants for slope, {{{m}}}, and y-intercept, {{{b}}}.
It also tells you that the slope is {{{m=-30}}}.
 
"People living in Fairbanks drink 3600 cups of hot chocolate per day when the temperature is 0 degrees celsius."
That gives you the value of {{{y}}} when {{{x=0}}}, which is the y-intercept,
{{{b=3600}}}
 
a. The expression that represents the number of cups of hot chocolate drunk per day as a function of degrees celsius is
{{{highlight(y=-30x+3600)}}} or the equivalent {{{highlight(y=3600-30x)}}} 
 
b. How many cups would they drink at 5 degrees celsius?
{{{x=5}}} --> {{{y=3600-30*5}}} --> {{{y=3600-150}}} --> 
{{{highlight(y=3450)}}} 
 
c. How many cups would they drink at 25 degrees celsius?
{{{x=25}}} --> {{{y=3600-30*25}}} --> {{{y=3600-750}}} --> 
{{{highlight(y=2850)}}} 
 
d. Write an equation to determine the temperature if 3000 cups of hot chocolate were consumed in a day.
{{{y=3000}}} --> {{{highlight(3000=3600-30x)}}}
 
e. Solve the equation to find the temperature if 3000 cups of hot chocolate were consumed in a day.
 --> {{{3000=3600-30x}}} --> {{{3000-3000+30x=3600-30x-3000+30x}}} --> {{{30x=600}}} --> {{{30x/30=600/30}}} --> {{{highlight(x=20)}}}

f. Is this answer reasonable? Explain.
It is very {{{highlight(reasonable)}}}.
At {{{0^o}}}{{{C}}} they drink {{{3600}}} cups.
As the temperature increases, hot chocolate consumption decreases.
At {{{5^o}}}{{{C}}} they drink less hot chocolate: {{{3450}}} cups.
Since {{{20^o}}}{{{C}}} is even warmer,
they should drink even less at {{{20^o}}}{{{C}}},
but not as little as the {{{2850}}} cups they drink on those very warm {{{25^o}}}{{{C}}} days.