Question

Richie and Phoebe are saving money to buy a new tv. They need at least $510 to purchase the new TV. Phoebe weeds yards and Richie walks dogs to earn money. Phoebe charges $12 each time she weeds a yard and Richie charges $9 each time he walks a dog. The number of dog walks that Richie has scheduled is no more than twice the number of yards Phoebe has scheduled to weed. Richie will walk at least 25 dogs.

Write a set of constraints to model the problem, with x representing the number of lawns weeded and y representing the number of dogs walked. (HINT: there are 3 constraint equations).

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Answer 1

Number of yards Phoebe weeds = x

Richie walks no more than 2 times the yards Phoebe does so y ≤ 2x

He will walk at least 25 dogs, so Y ≥25

Then they need to earn at least 510, so 12x + 9y ≥ 510

The three constraints are:

y ≤ 2x

Y ≥ 25

12x + 9y ≥ 510

Answer 2

• 12x +9y ≥ 510
• y ≤ 2x
• y ≥ 25

Explanation:

Phoebe earns 12x for her yard weeding, and Richie earns 9y for his dog walking. They want the sum of these earnings to be at least 510, so the first constraint inequality is ...

12x +9y ≥ 510

__

Richie plans to walk no more than 2x dogs, since y is the number of dogs he walks, the second constraint is ...

y ≤ 2x

__

Richie will walk at least 25 dogs, so ...

y ≥ 25