can someone help me on thiworked problem?Suppose that you take care of pets for vacationing neighbors each summer. You charge $15 per day to feed and walk a dog, and $5 per day to feed other pets....

can someone help me on thiworked problem?

Suppose that you take care of pets for vacationing neighbors each summer. You charge $15 per day to feed and walk a dog, and $5 per day to feed other pets. You know that you can care for at most 10 pets per day, and you want to earn at least $30 per day. Write a system of linear inequalities that describes the situation.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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Let us say you can care X number of dogs and Y number of other pets per day.

It is given that you can care at most 10 pets per day. This means the maximum number of pets you can care is 10.

The pets you can care is (X+Y).

Since the maximum is 10 we can say (X+Y) is less than or equal to 10.

`(X+Y)<=10`

 

You get $15 to feed a dog and $5 to feed an other pet per day.

Your earning per day is `(15X+5Y)` .

It is given that you earn at least $30 per day.

So your earnings per day is $30 or more.

`(15X+5Y)>=30`


We can further simplify this;

`(15X+5Y)/5>=30/5`

  `3X+Y >= 6`

 

So the system of inequalities that describe the situation is;

`(X+Y)<=10`

`3X+Y >= 6`

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