Word problems

Question

A dog collar is $7 and a cat collar is $4. We sold 22 collars for $124. How many of each did we sell?  

Please help.  

Answer 1

You have to convert the words into equations using the information you are given.

 

7D + 4C = 124

D + C = 22

 

With two unknowns you need two equations. Now use the second equation to express one of the unknown variables in terms of the other:

 

D = 22 - C  ..  and then substitute D in the first equation to give you one variable

 

7(22-C) + 4C = 124

154 - 7C + 4C = 124

154 - 124 = 7C - 4C

30 = 3C

C = 10

 

Therefore D = 22 - 10 = 12

 

You can prove that this is correct by solving the first equation: 7*12 + 4*10 = 124