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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 LaTeX: xx represent the number of cars Jamie washes. Let LaTeX: yy 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

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Edufirst

Answer:

  •    Part 1: 25x ≥ 600
  •    Part 2: 15y ≥ 600
  •    Part 3: y ≤ 40

Explanation:

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.

  •    25x

2. Money earned by Stella  making pecan pies for $15 each

   Let y represent the number of pies she makes

  •    15y

3. 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 ≤ 40

4. First question:

Part 1: Write a constraint (an inequality) to represent how much money Jamie needs for his trip

  •    25x ≥ 600

5. Second question:

Part 2: Write a constraint (an inequality) to represent how much money Stella needs for her trip.

  •    15y ≥ 600

6. Third question

Part 3: Write a constraint (an inequality) to represent the limitations of Stella's supplies.

From step # 3

  •    y ≤ 40

7. Conclusion

You 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 ≤ 40

The 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.

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