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the ratio of two numbers is 3:7. the product of these 2 numbers is 189. what is the smaller of these numbers?

 Sep 12, 2020
 #1
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3x=7y

xy=189

 

Are the equations. Solving, y=9 and x=21 so 9 is the answer.

 Sep 12, 2020
 #2
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More elaborate solution:

 

Let the two numbers be x and y, where x is smaller.

 

By the first sentence, 7x=3y --> x=3/7y.

 

We also know that xy=189 --> (3/7y)(y)=189 --> 3/7y^2=189 --> y^2=441 --> y=21,-21.

 

When y=21, we have 7x=3*21 --> x=9

 

When y=-21, we have 7x=3*-21 --> x=-9

 

So our solutions are (x,y)=(21,9) and (-21,-9)

 

The smallest possible number is then -9

 Sep 13, 2020

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