Question

Two numbers are in the ration 2is to 3. If 14 is added to each number then the ration becomes 12 is to 17. Find the smaller number

Answer 1

Answer:

Let the numbers be 2x and 3x.

2x+9 : 3x+9 = 3 : 4, or

4(2x+9) = 3(3x+9), or

8x+36 = 9x+27, or

x = 9.

So the numbers are 18 and 27.

Check: 18:27 is 2:3. Now add 9 to both to get 27 and 36 and their ratio = 3:4. Correct.

Answer 2

Let the numbers be 2x and 3x.

Let the numbers be 2x and 3x.2x+9 : 3x+9 = 3 : 4, or

Let the numbers be 2x and 3x.2x+9 : 3x+9 = 3 : 4, or4(2x+9) = 3(3x+9), or

Let the numbers be 2x and 3x.2x+9 : 3x+9 = 3 : 4, or4(2x+9) = 3(3x+9), or8x+36 = 9x+27, or

Let the numbers be 2x and 3x.2x+9 : 3x+9 = 3 : 4, or4(2x+9) = 3(3x+9), or8x+36 = 9x+27, orx = 9.

Let the numbers be 2x and 3x.2x+9 : 3x+9 = 3 : 4, or4(2x+9) = 3(3x+9), or8x+36 = 9x+27, orx = 9.So the numbers are 18 and 27.

Let the numbers be 2x and 3x.2x+9 : 3x+9 = 3 : 4, or4(2x+9) = 3(3x+9), or8x+36 = 9x+27, orx = 9.So the numbers are 18 and 27.18:27 is 2:3. Now add 9 to both to get 27 and 36 and their ratio = 3:4.