Answer:
250-5m=200+4m ; 5.56 months
Step-by-step explanation:
<u>Let's start this question by writing two expressions that depict the situation.</u>
Vance: 250-5m
This simply means that Vance currently weighs 250 pounds, and every month he is losing 5 pounds. (m=number of months)
Phillip: 200+4m
This is essentially the same thing. Phillips starting weight is 200, but here we use an addition sign because he is gaining 4 pounds every month as opposed to losing it.
To find the number of months it'll take for them to weigh the same, we just need to equate the values and solve for m.
<u>Our equation would then be:</u>
250-5m=200+4m
Let's solve the equation by bringing the variables to one side and the numbers to the other.
250-5m=200+4m
Subtract 4m from both sides
250-5m-4m=200+4m-4m
250-9m=200
Subtract 250 from both sides
250-250-9m=200-250
-9m=-50
Divide both sides by -9
m=5.556
So it will take about 5 months and a half to weigh the same.
Answer:
They will spend less at the sunny side hotel
Step-by-step explanation:
The attachment completes the question.
From the question, we understand that there are 4 individuals involved.
- Mr. Preston (1)
- Mrs. Preston (1)
- The children (2)
And they will spend one night
First, we need to calculate the expenses in Traveler's hotel.
(for 3 people)
(for 1 person)
(for 4 people)

Total Expenses



For Sunny Side hotel:
(for 4 people)

Total Expenses:


By comparison, they will spend less at the sunny side hotel.
It has to be wider than the first two arcs or else you will just get two circles side by side with point c in common. I usually measure it to be the length of a point between the c and j. It is a good point to get the arcs to intersect.
This ODE is separable, so you can write

Integrating both sides gives

and given the initial condition

, you have

so that the solution is
Solving for 'y'
2x - 2y + 5 = 0
Add 2y on both sides
2x + 5 = 2y
Divide by 2 on both sides
y = x + 5/2
y = x + 2.5
Solving for 'x'
2x - 2y + 5 = 0
Subtract 2x on both sides.
-2y + 5 = -2x
Divide 2x on both sides
x = y - 5/2
x = y - 2.5