SOLUTION: Pete and Repeat are brothers. Of course with names like Pete and Repeat they usually quarrel when it comes to making decisions. The brothers have decided they would like to open

Question 989537: Pete and Repeat are brothers. Of course with names like Pete and Repeat they usually quarrel when it comes to making decisions. The brothers have decided they would like to open a small neighborhood pet store. After many heated discussions they have decided to sell dogs, cats, and exotic fish(no turtles or birds). Together they have a $1000 to spend on animals for their venture. Pete thinks they have room for 100 animals in the store. Repeat knows that cats cost $5, dogs cost $10 and exotic fish cost $100(they are really unusual and large fish). "Pete declares we must buy a total of 100 Animals" Repeat argues back "But we need to spend all our money to get the best selection for our customers" Help the brothers determine how to stock their new pet store and make both brothers happy with their decision.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are six different solutions if you allow the case where one or more of the animal types are not represented at all, 5 valid solutions otherwise.

Let

represent the number of cats,

represent the number of dogs,

represent the number of fish.

Solve this by cases, where

takes on values in the range 0 through 10. If you wish to disallow the case where any animal type is not represented at all, then start at 1. For each value of z you choose, adjust the value of the constant term and then solve the 2X2 system for

and

. At some point, you will start getting a negative number for the

variable, so you can discard that value of

and anything larger.

John

My calculator said it, I believe it, that settles it

RELATED QUESTIONS
The ages of Pete and Tim combined are 66 years. Pete is 6 years younger than Tim. How (answered by Alan3354,checkley79)

Sandra and Pete are washing cars for a fundraiser. Working together, they can wash a car... (answered by AnlytcPhil)

Brothers Paul and Pete walk 2 miles to school from home. Paul can walk to school in 24... (answered by ankor@dixie-net.com)

Seymour Blossoms and Pete Moss plant flowers in a botanical garden. Working by himself it (answered by josmiceli)

Carla is 5 years old. Pete's age is the sum of Carla and Tyler's age. Tyler is 13 years... (answered by TimothyLamb)

Pauline and Pete agree to meet in Columbia. Pauline travels 120 miles, while Pete travels (answered by josgarithmetic,ikleyn,greenestamps)

Joe, Sarah, and Pete want to share a pizza, but there are 5 pieces left that are each... (answered by josgarithmetic)

in a bicycle race, pete gives joey a 500 meter advantage. Also, Pete agrees to start 15... (answered by josmiceli)

Judy and Pete are building a new house and want to carpet their living room, except for... (answered by richwmiller,carloslynn)