Solving problems using linear equations

Question

A pet shop have rabbits and gerbils for sale. They have 20 animals altogether. They sell two rabbits. Then one of the gerbils has twins. The shopn now has three times as many gerbils as rabbits. How many of each did they start with?

Answer 1

Hi Rebecca,

 

Start with an equation comparing the starting number of rabbits and gerbils:

 

R₁ + G₁ = 20    (Rabbits plus Gerbils equals 20 animals total)

 

Next, notice that 2 Rabbits are sold, and 2 Gerbils are born . . .

so you still have the same number of animals total . . . 20!

 

R₂ + G₂ = 20    (new amounts of Rabbits and Gerbils still equals 20)

 

Finally, an equation for the final situation:

 

G₂ = 3R₂    (number of Gerbils is 3 times the number of Rabbits)

 

Now you substitute:

 

R₂ + 3R₂ = 20

        4R₂ = 20        (combine like terms)

          R₂ = 5          (divide both sides by 4 to isolate the variable)

 

This means in the end, there were 5 Rabbits.  Since 2 were sold, originally there were

 

7 Rabbits    (7 - 2 = 5)

 

which means there were originally

 

13 Gerbils    (20 - 7 = 13)