Question

Jamie and Stella are saving money to sign up for a school trip to Washington, D.C. In order to sign

up for the trip, they must pay $600 upfront. Jamie earns his money by washing cars for $25 each.
Stella earns her money by making pecan pies for $15 each. Jamie earns more money than Stella
does because Stella only has enough supplies to make 40 pies. Let I represent the number of cars
Jamie washes. Let y represent the number of pies Stella makes.
Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip.
Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.
Part 3: Write a constraint (an inequality) to represent the relationship between Jamie's earnings
and Stella's earnings.
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 1

Explanation:

Let
`I` be the number of cars Jaime washes.

Given that Jamie earns his money by washing cars for $
`25` each.

Total income for
`I` cars is [$tex]25I[/tex]

Let
`y` represent the number of pies Stella makes.

Given that Stella earns her money by making pecan pies for $
`15` each.

Total income for
`y` pies is $
`15y`

Jamie needs atleast $
`600` for his trip.

So,
`25I\geq600`

`I\geq 24`

Stella needs atleast $
`600` for his trip.

So,
`15y\geq600`

`y\geq 40`

Given that Jamie earns more money than Stella.

So,
`25I\geq 15y`

`5I\geq 3y`

If Stella makes
`40` pies,she makes
`15* 40=600` which is just required.

So,Stella can signup only if she sells
`40` pies.