Question

Carmen is 12 years older than David. Five years ago the sum of their ages was 28. How old are they now?

Answer 1

Answer:

David = 13, Carmen = 25

Step-by-step explanation:

let davids age be = x

Carmen's age = x + 12

five years age David's age = x-5

Carmens age = x+12-5 = x+7

five years age the sum of their age = 28

x + 7 + x - 5 = 28

2x + 2 = 28

2x = 26

x = 26/2 = 13

their present age David = 13

Carmen = 13 + 12 = 25

five years ago David = 13 -5 = 8

Carmen age = 25 -5 = 20

20 + 8 = 28

Answer 2

Given: Carmen is 12 years older than David. Five years ago the sum of their ages was 28.

To find: Their age now.

Solution:

• Let the age of Carmen be equal to x and the age of David be equal to y.
• If Carmen is 12 years older than David, an equation can be formed as follows,

       $x = 12 + y$

       $x - y = 12$

• Five years ago, the age of Carmen would be (x - 5) and the age of David would be (y - 5).
• According to the given question, the sum of their ages five years ago summed up to give 28.
• So, $(x - 5) + (y - 5) = 28$

               $x + y = 38$

• On equating the two equations formed, the value of x is found to be 25 and y is found to be 13.

Therefore, Carmen is 25 years old and David is 13 years old.