Question

Help please!!!!!...........................

Answer 1

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 $T$) is that any total amount of money must be equal or more than $600, which in maths notation reads:

$T\geq 600$

where $\geq$ 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) $x$, Jamie makes $25, thus for Jamie we have:

J: $25x$

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) $y$, Stella makes $15, thus for Stella we have:

S: $15y$

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

$15y$ is true, for $y\leq 40$

where $y\leq 40$ is the constraint on Stellas possible profits and $\leq$ 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:  $25x$

*provided that $25x\geq 600$ (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:  $15y\geq600$ and  $y\leq40$

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 $y\geq 40$ (Jamie) ∩ $y\leq40$ (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 $15y$, and the total amount needed for the trip upfront is denoted by $T\geq 600$ 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:

$15y\geq 600\\y\geq \frac{600}{15}\\ y\geq 40$

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!