the ratio of two numbers is 3:7. the product of these 2 numbers is 189. what is the smaller of these numbers?
Are the equations. Solving, y=9 and x=21 so 9 is the answer.
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