Answer:Part 1: 25x ≥ 600
Part 2: 15y ≥ 600
Part 3: y ≤ 40
Part 4: Yes, she can afford to sign up the contract with the money she earns, because she can earn $ 15/pie × 40 pie = $ 600.
Step-by-step explanation:
To find the solutions to the questions, you must translate the verbal statements into algebraic expressions, equations or inequalities.
Let's tackle each statement one by one:
1. Jamie and Stella are saving money
Name the variable money as M.
2. They must pay $600 upfront
Then, that sets the value of M to 600: M = 600
3. Jamie earns his money by washing cars for $25 each.
Let x represent the number of cars Jaime washes.
Then, the money that he earns is:
25x
4. Stella earns her money by making pecan pies for $15 each.
Let y represent the number of pies she makes
The, the money she earns is:
15y
5. Stella only has enough supplies to make 40 pies.
That is a constraint because it imposes an upper limit on y, which permits to write an inequality using the symbol ≤, since y can take any integer value up to 40.
y ≤ 40
6. Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip
25x ≥ 600
7. Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.
15y ≥ 600
8. Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.
This is the same inequality written in the step # 5.
y ≤ 40
9. Part 4: Can Stella afford to sign up for the trip with the money she earns?
To answer that, you must solve for the inequalities that represent Stella's situation:
From step 4 and 7: 15y ≥ 600
Solving that inequality:
Divide both sides by 15: y ≥ 600 / 15
Simplifying: y ≥ 40
From step 8: y ≤ 40
So, the intersection of the two solutions is y = 40, which means that Stella can afford to sign up for the trip with the money she earns, as she will be able to make 40 pies, which represents a revenue of $ 15 / pie × 40 pie = $ 600.