Question

Carla is 5 years old and Jim is 13 years younger than Peter. One year ago, Peter's age was twice the sum of Carla's and Jim's age. Find the present age of each one of them

Answer 1

$\textbf{SOLUTION:}$

$<b>Let x be Peter's age now. Hence the present age of Carla, Jim and Peter are given by$

Carla : 5 
Peter : x 
Jim : x - 13 

One year ago their ages were 
Carla : 5 - 1 = 4 
Peter : x - 1 
Jim : x - 13 - 1 = x - 14 

One year ago, Peter's age was twice the sum of Carla's and Jim's age which is written mathematically as 
x - 1 = 2 (4 + x - 14) 

Simplify and expand the right side of the above equation
x - 1 = 2 (x - 10) 
x - 1 = 2x - 20 

Add + 20 to both sides and simplify 
x - 1 + 20 = 2x - 20 + 20 
x + 19 = 2x 

Subtract x to both sides and simplify 
x + 19 - x = 2x - x 
19 = x , Peter's age now 
Jim's age: x - 13 = 19 - 13 = 6

Carla's age: 5

Answer 2

Answer:

Let x be Peter's age now. Hence the present age of Carla, Jim and Peter are given by

Carla : 5

Peter : x

Jim : x - 13

One year ago their ages were

Carla : 5 - 1 = 4

Peter : x - 1

Jim : x - 13 - 1 = x - 14

One year ago, Peter's age was twice the sum of Carla's and Jim's age which is written mathematically as

x - 1 = 2 (4 + x - 14)

Simplify and expand the right side of the above equation

x - 1 = 2 (x - 10)

x - 1 = 2x - 20

Add + 20 to both sides and simplify

x - 1 + 20 = 2x - 20 + 20

x + 19 = 2x

Subtract x to both sides and simplify

x + 19 - x = 2x - x

19 = x , Peter's age now

Jim's age: x - 13 = 19 - 13 = 6

Carla's age: 5