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 [tex]T[/tex]) is that any total amount of money must be equal or more than $600, which in maths notation reads:
[tex]T\geq 600[/tex]
where [tex]\geq[/tex] means More or Equal to.
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) [tex]x[/tex], Jamie makes $25, thus for Jamie we have:
J: [tex]25x[/tex]
Similarly we know that Stella makes pecan pies and for each pie she sells she makes $15, so we can say that for every pecan pie (denoted by) [tex]y[/tex], Stella makes $15, thus for Stella we have:
S: [tex]15y[/tex]
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. Therefore we can now say that
[tex]15y[/tex] is true, for [tex]y\leq 40[/tex]
where [tex]y\leq 40[/tex] is the constraint on Stellas possible profits and [tex]\leq[/tex] means Less or Equal to.
Now lets start answering the questions:
Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.
Answer: [tex]25x[/tex]
*provided that [tex]25x\geq 600[/tex] (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: [tex]15y\geq600[/tex] and [tex]y\leq40[/tex]
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 [tex]y\geq 40[/tex] (Jamie) ∩ [tex]y\leq40[/tex] (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 [tex]15y[/tex], and the total amount needed for the trip upfront is denoted by [tex]T\geq 600[/tex] 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:
[tex]15y\geq 600\\y\geq \frac{600}{15}\\ y\geq 40[/tex]
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!
