Question

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

Answer 1

9.

Explanation:

I am assuming that the two numbers are positive.

Let the numbers be 3x and 7x.

Then 3x * 7x = 19

21x^2 = 189

x^2 = 9

x = 3.

So the smaller of these numbers is 3*3 = 9.

Answer 2

9 if that does not work try - 21

Explanation:

Let the two numbers be x and y

x/y = 3/7 which means that x is the smaller number.

x*y = 189

Cross multiply the top equation

7x = 3y

Divide by 7

x = 3/7 ^ y

x*y = 189

(3/7 y) * y = 189

Multiply by 7

3y^2 = 189*7

3y^2 = 1323

Divide by 3

y^2 = 441

Take the square root of both sides

y = 21

The question is a bit ambiguous. You could use - 9 and - 21 in which case the smallest number is -21. I think they intend 9 however.

x = 3/7 * 21

x = 3*3

x = 9

Check

x*y = 9 * 21 = 189