Question

Two numbers are consecutive positive multiples of 3. Three times the larger of the numbers is 7/10of 5 times the smaller. What are the numbers?

Answer 1

18 and 21

Explanation:

Let the smaller number = 3x

Let the larger number = 3x + 3

The three and the plus 3 insure that the numbers are multiples of 3 and are consecutive.

3* (3x + 3) = 7/10 * 5 (3x) Multiply both sides by 10

30*(3x + 3) = 7 * 5 * 3x Remove the brackets

90x + 90 = 7 * 5 * 3x Combine the right

90x + 90 = 105x Subtract 90x from both sides.

-90x -90x

90 = 15x Divide by 15

x = 90/15

x = 6

Let's see if it works.

3*(3x + 3) = 3*(18 + 3) = 3 * 21 = 63

7/10 * 5 *3x = 7/10 * 5 * 3*6 = 630 / 10 = 63