Answer-
Set of constraints to model the problem are,
[tex]12x+9y\geq 510[/tex]
[tex]y \leq 2x[/tex]
[tex]y \geq 25[/tex]
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,
[tex]\text{Earnings of Gwen} = 12x[/tex]
[tex]\text{Earnings of Fabio} = 9y[/tex]
[tex]\text{Total earning} = 12x+9y[/tex]
They need at least $510 to purchase the new gaming station, means they need $510 or more than $510.
The equation for this is,
[tex]12x+9y\geq 510[/tex]
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,
[tex]y \leq 2x[/tex]
3.
Fabio will walk at least 25 dogs, means y must be greater than of equal to 25.
The equation for this is,
[tex]y \geq 25[/tex]
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:
[tex]y>25[/tex]
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:
[tex]y<2x[/tex]
The total money that they need after doing all the work should be at least $510.00.
[tex]12x+9y>510[/tex]
