Question

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

Answer 1

See solution :)

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 (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!