# Puzzle

G

#### Guest

##### Guest
How do I solve the following puzzle?

Two alligator breeders were talking one day, and in the course of their conversation they noticed a curious coincidence. If alligator breeder #1 were to sell alligator breeder #2 seven alligators, then breeder #1 would have exactly as many alligators as breeder #2. On the other hand, if alligator breeder #2 were to sell alligator breeder #1 seven alligators, then breeder #1 would have exactly twice as many alligators as breeder #2. How many alligators did each breeder have?

My daughter was given this puzzle to solve for her math class. How do I help her solve it?

#### Denis

##### Senior Member
x = Breeder#1's alligators
y = Breeder#2's alligators

x - 7 = y + 7
x = y + 14 

2(y - 7) = x + 7
2y - 14 = x + 7
2y - x = 21 

Substitute  in :
2y - (y + 14) = 21
2y - y - 14 = 21
y = 21 + 14
y = 35

: x = 35 + 14 = 49

Proof:
49 - 7 = 35 + 7

49 + 7 = 2(35 - 7)

#### Unco

##### Senior Member
Let x be the number of alligators breeder #1 has
Let y be the number of alligators breeder #2 has

"If alligator breeder #1 were to sell alligator breeder #2 seven alligators, then breeder #1 would have exactly as many alligators as breeder #2"

translates to
x - 7 = y + 7 (#1 las lost 7, and #2 has gained 7; they now have an equal number)
ie.
x - y = 14

"if alligator breeder #2 were to sell alligator breeder #1 seven alligators, then breeder #1 would have exactly twice as many alligators as breeder #2."

translates to
...2(y - 7) = x + 7 (#2 has lost 7, #1 has gained 7; #2 has twice the number of #1)
ie. 2y - 14 = x + 7
ie. x - 2y = -21

"How many alligators did each breeder have? "
Find x and y. We have two equations to solve

x - y = 14
x - 2y = -21

Arrange one to make x the subject and substitute this into the other equation to solve for y. Substitute this y value into one of the equations to find x.

Good luck!

Edit: Denis is too fast for me!

G

#### Guest

##### Guest
Thank you so much for your help and for the detailed explanation. Now I can help her set the problem up and then let her solve it and then check her answer. This site is great. I will be back.