Question

Three years ago Tom was twice as old as Jean, and in two years the sum of their ages will be 28 years. Find their present ages.

Answer 1

Answer:

Tom is 15 years old and Jean is 9 years old

Step-by-step explanation:

Let call:

x: the age of Tom

y: the age of Jean

From the sentence: three years ago Tom was twice as old as Jean, we get the first equation:

(x-3)=2(y-3)

Solving for x:

x=2y-6+3

x=2y-3

From the sentence: in two years the sum of their ages will be 28 years, we get the second equation:

(x+2)+(y+2)=28

Solving:

x+y+4=28

x+y=28-4

x+y=24

Now, we have two equations with two incognites:

equation 1: x=2y-3

equation 2: x+y=24

For finding the values of x and y we need to replace the x = 2y-3 on the second equation and solve for y, as following:

(2y-3)+y=24

2y+y-3=24

3y=27

y=27/3

y=9

Then, we Replace y=9 on the first equation and get:

x=2(9)-3

x=18-3

x=15

Now, we have the values of x and y that satisfy the two formulate equation, so the answer is x equal to 15 and y equal to 9. So, Tom is 15 years old and Jean is 9 years old

Answer 2

Answer:

Jean is 9 and Tom is 15.

Step-by-step explanation:

3 years ago, Tom was 12 and Jean was 6, hence Tom was twice as old as Jean.  

Since that was their age 3 years ago, they are currently 15 (Tom) and 9 (Jean).  

Add 2 years to each of these ages, you get 17 and 11.

17 + 11 = 28