basic word problem help

Question

ok, its been a long time since i've done algebra (20 years). Here is the problem:

 

Woman sells dog leashes and collars on the weekends at dog shows. One weekend she sold a total of 34 leashes. The number of leashes she sold was two less than three times the number of collars. How many of each did she sell?

 

This is how I solved it=

 

3 ( X - 2 ) = 34

3X - 6 = 34

 

3x = 40

 

40 / 3 

 

X= 13

 

Leashes are 13- 2 = 11

 

Collars = 3 (11)

 

But that gets me 44 (when I add the two numbers back and not the 34). Where am I going wrong?

 

Thanx

Answer 1

34=3x-2

 

"Thirty four leashes (34) equals (=) two less than (-2) three times the number of collars (3x)"

 

Add two to both sides:

36=3x

Divide both sides by 3:

12=x

 

Check:

34=3(12)-2

34=36-2

34=34

 

Please contact me if you have any questions. Thanks!

 

Answer 2

Q: Woman sells dog leashes and collars on the weekends at dog shows. One weekend she sold a total of 34 leashes. The number of leashes she sold was two less than three times the number of collars. How many of each did she sell?

 

A: The problems states that she sold a total of 34 leashes. It also says that the number of leashes sold was two less than three times the number of collars. 

 

Let L = number of leashes and C = number of collars. 

 

L is stated in the problem. L = 34.

 

L = 3C - 2.

 

Solving for C -> C = 1/3*(L + 2).

 

L = 34.

 

C = 1/3*(L + 2).

 

I think you misunderstood the problem. The number of leashes is already stated in the problem. The trick is to find the number of collars by forming an equation from the information given in the question. 

Answer 3

let C=# of collars

34=3C-2

36=3C

12=C, the number of collars

34 is 2 less than 3x12 which equals 36

 

If you meant to say that 34 is the total number of leashes and collars sold, then we do the problem differently.

 

L+C=34

L+2=3C

L=3C-2

substitute 3C-2 for L in the first equation

3C-2+C=34

4C-2=34

4C=36

C=9 collars

34-9=25 leashes

25 is 2 less than 3x9=27