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Nataliya [291]
2 years ago
6

You and your friend leave your houses at the same time to meet at a restaurant. The distance (in miles) your friend is from the

restaurant is given by y=-70x+140,where x is the number of hours since your friend left home. You live 80 miles from the restaurant and arrive at the same time as your friend. Write a linear equation that represents your distance from the restaurant.
Mathematics
1 answer:
Katen [24]2 years ago
6 0

Answer:

y = 80 -40x

Step-by-step explanation:

The given equation shows the friend arrives at the restaurant (y=0) when x=2. That is, half the initial distance to the restaurant is covered in each hour of travel time.

If I take 2 hours to travel the 80 miles from my house, my distance will decrease at the rate of 40 miles per hour. My distance from the restaurant can be represented by ...

... y = -40x +80

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Answer:

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  •    Part 2: 15y ≥ 600
  •    Part 3: y ≤ 40

Explanation:

Verbal statements must be translated into algebraic expressions, equations or inequalities.

<u>1. Money earned by Jamie washing cars for $25 each</u>

   Let x represent the number of cars Jaime washes.

  •    25x

<u>2. Money earned by Stella  making pecan pies for $15 each</u>

   Let y represent the number of pies she makes

  •    15y

<u>3. Constraint on the number of pies that Stella can make because she only has enough supplies to make 40 pies</u>.

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

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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:

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  •    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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3 years ago
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