Question

Beth is 2 years older than Jimmy, and in 3 years the sum of their ages will be twice as much as the sum of their ages 3 years ago. Find their present ages.

Answer 1

Jimmy is 8
Beth is 10

Answer 2

Solving by means of a system of equations, it is obtained that Beth's age is 10 years and Jimmy's age is 8 years.

First, you need to know the definition of a system of equations. A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.

In this case, the two unknowns or variables to calculate are:

• B: age of Beth
• J: age of Jimmy

Beth is 2 years older than Jimmy. Expressed mathematically, it is obtained:

B= J +2

On the other side, in 3 years the sum of their ages will be twice as much as the sum of their ages 3 years ago. Expressed mathematically, it is obtained:

(B +3) + (J+3) = 2*[(B -3) + (J-3)]

Then the system of equations to solve is:

`\left \{ {{B= J +2} \atop {(B +3) + (J+3) = 2*[(B -3) + (J-3)]}} \right.`

The substitution method consists of solving or isolating one of the unknowns and substituting its expression in the other equation. In this case, substituting expression for the variable B of the first equation in the second equation, you obtain:

(J+2 +3) + (J+3) = 2*[(J+2 -3) + (J-3)]

Solving:

J +5 + J +3= 2*[ J -1 + J -3]

2*J + 8= 2*[2*J - 4]

2*J +8= 2*2*J - 2*4

2*J +8= 4*J - 8

8+8= 4*J - 2*J

16= 2*J

16÷2= J

8= J

Now, replacing this value in the first equation:

B= J+2

B= 8 +2

B=10

Remembering that B represents Beth's age and J represents Jimmy's age, so Beth's age is 10 years and Jimmy's age is 8 years.