Answer:
See solution :)
Step-by-step explanation:
Let us first analyse our information given. The question tells us that each person, (i.e. Jamie and Stella) should pay $600 upfront. Thus, our first constraint (lets call it ) is that any total amount of money must be equal or more than $600, which in maths notation reads:
<em>where means More or Equal to. </em>
We also know that Jamie washes care for $25 dollars and if represented in math notation, we can say that for every car (denoted by) , Jamie makes $25, thus for Jamie we have:
J:
Similarly we know that Stella makes pecan pies and for each pie she sells she makes $15, so we can say that<em> for every pecan pie (denoted by) , Stella makes $15, thus for Stella we have:</em>
S:
However, we also know that Stella does not have enough supplies for more than 40 pies, which puts a constraint on the amount of money she can make by selling pecan pies. <em>Therefore we can now say that</em>
is true, for
<em>where is the constraint on Stellas possible profits and
means Less or Equal to. </em>
<u>Now lets start answering the questions: </u>
Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.
Answer:
*provided that (in order to make the neccesary profit)
Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.
Answer: and
Part 3: Write a constraint (an inequality) to represent the relationship between Jamie's earnings and Stella's earnings.
Answer: Since Stella can not make more than 40 pies, the solution intersection between Jamie and Stella is (Jamie) ∩
(Stella), thus y=40.
Part 4: Can Stella afford to sign up for the trip with the money she earns? Explain your answer and show any work that might support your answer.
Answer: We know that Stella's pie making is denoted by , and the total amount needed for the trip upfront is denoted by
therefore to find if Stella can afford to sign up, we need to find the amount of pies Stella needs to produce, in order to make a profit of at least $600. Thus we write:
Since the number of pies Stella needs to make, to gain a profit of $600 is 40 pies, and we know that Stella can make a maximum of 40 pies with the supplies she already has, we can conclude that Stella can make the necessary money to make her trip to Washington!