If the number of puppies plus guppies equals 58, frogs plus puppies equals 17, and guppies plus frogs equals equals 51. How many of each animal are there?

Question

I need to find out how many puppies, guppies, and frogs there are in the pet shop.

Answer 1

Let x = the number of guppies

Let y = the number of puppies

Let z = the number of frogs

x + y = 58 (eq#1)

y + z = 17 (eq#2)

x + z = 51 (eq#3)     Subtract equations #2 and #3.

 

     y + z = 17

-(x + z) = -51

y - x = -34 (eq#4)   Add equations #1 and #4.

 

y + x = 58

y - x = -34 

2y = 24

y = 12 (eq#5)     Substitute eq#5 into eq#2.

 

y + z = 17

12 + z = 17

z = 5 (eq#6)     Substitute eq#6 into eq#3.

 

x + z = 51

x + 5 = 51

x = 46