The equation that shows the profit earned for selling popcorn for x hours is y = $15m - $20
From the equation of the linear function given y = mx + b
y indicates the profit earned and x represents the time in hours.
From the question,
After 3 hours, the popcorn stand earned a profit of $25.
∴ The equation becomes $25 = 3m + b ------ (1)
and after 6 hours, the profit was $70.
∴ The equation becomes $70 = 6m + b ------- (2)
Now, we will solve the two equations simultaneously
From the first equation
$25 = 3m + b
We can write that
b = $25 - 3m ------- (3)
Substitute this into the second equation
$70 = 6m + b
We get
$70 = 6m + ($25 - 3m)
$70 = 6m + $25 - 3m
$70 - $25 = 6m - 3m
$45 = 3m
∴ m = $45 ÷ 3
m = $15
Now, substitute the value of m into equation (3)
b = $25 - 3m
b = $25 - 3($15)
b = $25 - $45
b = -$20
∴ m = $15 and b = -$20
Putting these values into the equation y = mx + b we get
y = $15m +(- $20)
∴ y = $15m - $20
Hence, the equation that shows the profit earned for selling popcorn for x hours is y = $15m - $20
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Answer:
Step-by-step explanation:
Let:
This is an exact differential equation because:
With this in mind let's define f(x,y) such that:
and
So, the solution will be given by f(x,y)=C1, C1=arbitrary constant
Now, integrate 
with respect to x in order to find f(x,y)
where g(y) is an arbitrary function of y
Let's differentiate f(x,y) with respect to y in order to find g(y):
Now, let's replace the previous result into :
Solving for 
Integrating both sides with respect to y:
Replacing this result into f(x,y)
Finally the solution is f(x,y)=C1 :
Answer:
3/5=18/30
Step-by-step explanation:
3/5*6/6=18/30
