Question

Please answer soon.

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.

Please show the work. Thanks

Answer 1

Answer-

Set of constraints to model the problem are,

$12x+9y\geq 510\\y \leq 2x\\y \geq 25$

Solution-

Let us assume,

x = the number of lawns weeded by Gwen,

y = the number of dogs walked by Fabio.

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

$\text{Earnings of Gwen} = 12x\\\text{Earnings of Fabio} = 9y\\\text{Total earnings of Gwen and Fabio} = 12x+9y$

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

An equation for this situation will be,

$12x+9y\geq 510$

The number of dog walked by 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.

An equation for this situation will be,

$y \leq 2x$

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

An equation for this situation will be,

$y \geq 25$