Find Number of Dogs

[nycmathdad]

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?

Let me see.

Note: twice as many dogs as cats in March:

Dogs = 2x

Cats = x

In April:

Dogs = 2(2x) + 3x

Total number of pets sold = 500

Here is my equation:

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

10x = 500

x = 500/10

x = 50

In March, the store sold twice as many dogs as cats. Here, x represents the number of cats. Twice that amount is 100. I say the number of dogs sold in March is 100.

You say?

 

[jonah1]

Beer soaked ramblings follow.

...
You say?

I say you should be done with mind numbing trivial stuff like this after 14 years of Precalculus review. You should be doing something more challenging.

 

[HOI]

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?

Let me see.

Note: twice as many dogs as cats in March:

Dogs = 2x

Cats = x

In April:

Dogs = 2(2x) + 3x

No. The number of dogs sold was 2(2x)= 5x and the number of cats sold was 3x.
The total number of pets sold in April was 2(2x)+ 3x= 7x.

Total number of pets sold = 500

Here is my equation:

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

10x = 500

x = 500/10

x = 50

In March, the store sold twice as many dogs as cats. Here, x represents the number of cats. Twice that amount is 100. I say the number of dogs sold in March is 100.

You say?

Yes, that is correct. It would be a good idea to check your work in the words of the original problem:1
"A certain pet store sells only dogs and cats. In March, the store sold twice as many dogs as cats.
If the store sold 50 cats and 100 dogs in March then, yes, the store sold twice as many dogs as cats.

"In April, the store sold twice the number of dogs that it sold in March,"
So in April the store solve 2(100)= 200 dogs.

"and three times the number of cats that it sold in March."
So the store sold 3(50)= 150 cats in March

"If the total number of pets the store sold in March and April combined was 500"
50+ 100+ 200+ 150=300+ 200= 500. Yes, that checks.

It was intelligent of you to write 2x= 100 dogs as the answer. A lot of people would have arrived at "x= 50" and stopped there!

 

[nycmathdad]

No. The number of dogs sold was 2(2x)= 5x and the number of cats sold was 3x.
The total number of pets sold in April was 2(2x)+ 3x= 7x.


Yes, that is correct. It would be a good idea to check your work in the words of the original problem:1
"A certain pet store sells only dogs and cats. In March, the store sold twice as many dogs as cats.
If the store sold 50 cats and 100 dogs in March then, yes, the store sold twice as many dogs as cats.

"In April, the store sold twice the number of dogs that it sold in March,"
So in April the store solve 2(100)= 200 dogs.

"and three times the number of cats that it sold in March."
So the store sold 3(50)= 150 cats in March

"If the total number of pets the store sold in March and April combined was 500"
50+ 100+ 200+ 150=300+ 200= 500. Yes, that checks.

It was intelligent of you to write 2x= 100 dogs as the answer. A lot of people would have arrived at "x= 50" and stopped there!

In your reply, you said 2(2x) = 5x. I assume this to be a typo. I got the right answer. Another check for me.