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 x 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 limitations of stella's supplies.

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.

Jamie: His inequality would look like this:  25x >= 600

Stella: Her inequality would look like this: 15y >= 600

Her limitations would be listed as: y=40

Yep. Stella has plenty of money by baking 40 pies; $600.

We can back that up by breaking this down. So. We know that it cost $600 to pay upfront and Jamie makes $25 per car he washes. Stella would make $15 for every pie she baked. So simply, let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes. Easy.

Since the cost for washing one car is $25

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600. We know that. Now, lets see their profit margins.

Since the cost for making one pie is $15

Therefore, the cost of making y pies is 15y.

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600 so with that being the case... 15y>=600

We all know the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. So y<=40

Bam.

In order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for . So our end project looks like this: 15y = 600 y = 600/15 = 40

The minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

Step-by-step explanation:

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)