Fabio and gwen are saving money to buy a new gaming station. they need at least $510 to purchase the new gaming station. gwen weeds yards and fabio walks dogs to raise money. gwen charges $12 each time she weeds a yard and fabio charges $9 each time he walks a dog. the number of dog walks that fabio has scheduled is no more than twice the number of yards gwen has scheduled to weed. fabio 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.

Answer-

Set of constraints to model the problem are,

Solution-

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

1.

As, Gwen charges $12 each time she weeds a yard and Fabio charges $9 each time he walks a dog,

They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.

The equation for this is,

2.

The number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, means

y must be less than or equal to 2x.

The equation for this is,

3.

Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.

The equation for this is,

Explanation:

Lets break the problem into steps and observe the constraints:

So Fabio and Gwen they are trying to save money and altogether they need at least $510.00.

Gwen charges $12.00 each time she weeds a yard.

Fabio charges $9.00 each time he walks a dog.

Fabio will walk at least 25 dogs. Here, 'x' represents the number of lawns weeded and 'y' represents the number of dogs walked.

Now talking about constraints:

Fabio will walk at least 25 dogs, so that implies:

Also, the number of dog walks that Fabio has scheduled is no more than twice the number of yards Gwen has scheduled to weed, that implies:

The total money that they need after doing all the work should be at least $510.00.

yes

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