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Question 1176355: Teena's dog, Popoy, wagged his tail. Poppy had never seen so many dogs at once. Teena counted up all the dogs at the dog show: the number is greater than 195; the number is less than 300; if you count by l0s you say its name; it can be divided evenly by 3 and 9. How many dogs did Teena count?
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
We're told that "if you count by l0s you say its name", which means that the number must end with a 0.
Counting by 10s is where we start at 10 and increase by 10 each time: 10,20,30,40,50,...
If a number is a multiple of 10, then it ends with a 0.
This is another way of saying 10 is a factor of the mystery number.
The clue that "it can be divided evenly by 3 and 9" means 3 and 9 are factors of this mystery number.
Because 9 and 10 are factors, this makes 9*10 = 90 a factor of the number.
Let's count by 90
90, 180, 270, 360, ...
The red value 270 fits the criteria that we're between 195 and 300. So we stop here because we found the answer.
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Or we could look at it like this:
90x = mystery number, since 90 is a factor
x = some positive whole number
195 < 90x < 300
195/90 < 90x/90 < 300/90 ......... divide all parts by 90
2.167 < x < 3.333
because x is a positive whole number, we can see that only x = 3 works in 2.167 < x < 3.333
In other words, 2.167 < x < 3.333 becomes 2.167 < 3 < 3.333 which is true.
Since x = 3, we know the mystery number is 90x = 90*3 = 270
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Answer: 270
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