Number of Dogs Sold in March

[nycmathguy]

A certain pet store sells only dogs and cats. In March, the store sold twice as many dogs as cats. In April, the store sold twice the number of dogs that it sold in March, and three times the number of cats that it sold in March. If the total number of pets the store sold in March and April combined was 500, how many dogs did the store sell in March?

(A) 80
(B) 100
(C) 120
(D) 160
(E) 180

Let me see.

Twice as many dogs as cats in March:

Dogs = 2x

Cats = x

In April, twice as many dogs as it sold in March:

Dogs = 2(2x)

Three times the number of cats it sold in March:

Cats = 3x

Total number of pets sold = 500.

Here is my equation:

2(2x) + 3x = 500

Solving for x leads to a decimal answer, which is wrong.

Stuck here....

Someone suggested following equation:

2(March) + March + 3(March) + March = 500

This leads to the following equation:

2(2x) + 2x + 3x + x = 500

If the suggestion is correct, why add March and April?

 

[MathLover1]

your equation is correct

2(March) + March + 3(March) + March = 500-> this one is also correct, but you use March=x (not 2x)

2(x) + x + 3(x) + x = 500

you ask "why add March and April?" -> simply because dogs and cats are sold in both months

 

[nycmathguy]

your equation is correct

2(March) + March + 3(March) + March = 500-> this one is also correct, but you use March=x (not 2x)

2(x) + x + 3(x) + x = 500

you ask "why add March and April?" -> simply because dogs and cats are sold in both months

The equation 2(March) + March + 3(March) + March = 500 is not my equation. I simply used March in place of x. This equation with the word March in it derives from the equation that someone else suggested.

Here is the suggested equation:

2(2x) + 2x + 3x + x = 500

I don't understand why the suggested equation is right and my original equation is wrong.

Original Equation:

2(2x) + 3x = 500

Of course, solving for x here leads to a decimal answer, which is incorrect.

You say?

 

[MathLover1]

2(March) + March + 3(March) + March = 500

you say 2(2x) + 2x + 3x + x = 500 =>why you using ones March=2x and the other time March=x?

correct version is: March=x

then you have 2(x) + x + 3x + x = 500

 

[nycmathguy]

2(March) + March + 3(March) + March = 500

you say 2(2x) + 2x + 3x + x = 500 =>why you using ones March=2x and the other time March=x?

correct version is: March=x

then you have 2(x) + x + 3x + x = 500

Conclusion:

Question is poorly worded like most word problems.

 

[HallsofIvy]

No, the problem was perfectly well worded- your attempted solution was poorly worded.

For example, at one point you say "Dogs= 2x" and at another "Dogs= 2(2x)". That is, at best, misleading. What you should have written was "Dogs in March= 2x" and "Dogs in April= 2(2x)", making it clear that those are different quantities.

 

[nycmathguy]

No, the problem was perfectly well worded- your attempted solution was poorly worded.

For example, at one point you say "Dogs= 2x" and at another "Dogs= 2(2x)". That is, at best, misleading. What you should have written was "Dogs in March= 2x" and "Dogs in April= 2(2x)", making it clear that those are different quantities.

Understood.