MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

Answer: Part 1: 25x ≥ 600 Part 2: 15y ≥ 600 Part 3: y ≤ 40Explanation:Verbal statements must be translated into algebraic expressions, equations or inequalities.1. Money earned by Jamie washing cars for $25 each Let x represent the number of cars Jaime washes. 25x2. Money earned by Stella making pecan pies for $15 each Let y represent the number of pies she makes 15y3. Constraint on the number of pies that Stella can make because she only has enough supplies to make 40 pies.Write an inequality using the symbol ≤, since y can take any integer value up to 40. y ≤ 404. First question: Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip 25x ≥ 6005. Second question:Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip. 15y ≥ 6006. Third questionPart 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.From step # 3 y ≤ 407. ConclusionYou can solve the inequalities fo find whether Stella can or not afford the trip:Solve for the inequalities that represent Stella's situation: 15y ≥ 600 y ≥ 600 / 15 y ≥ 40 From step 6: y ≤ 40The solution set is the intersection of the two solutions:y ≥ 40 ∩ y ≤ = 40 = 40. Interpretation: Stella will be able to make 40 pies, which represents a revenue of $ 15 / pie × 40 pie = $ 600, so she will be able to make the trip.