Question

Drew is 3 years younger than his brother, Jimmy. The sum of the brothers' ages is 21 1. Draw a bar model to represent this situation.​

Answer 1

The first step to solving a story problem is identifying variables.  For this problem, I will identify the variables as:

D = Drew's age

J = Jimmy's age

Once the variables are identified, we need to find as many equations as we have variables.  Since we have two variables, we will have to write two equations.

Since Drew is 3 years younger than Jimmy: D + 3 = J

Since the sum of the brothers' ages is 21:  D + J = 21

Once I have two equations is two variables, I can solve the system using either substitution method or elimination  method.  For this problem, I will use substitution method.

D + J = 21                       Equation 2

D + (D + 3) = 21              Substitution of value of J from equation 1 into equation 2

D + D + 3 = 21                Associative property of addition

2D + 3 = 21                    Simplify

2D + 3 - 3 = 21 - 3          Subtract 3 from each side

2D = 18                          Simplify each side

2D/2 = 18/2                    Divide each side by 2

D = 9                             Simplify each side

Now that we have D, we can substitute it into equation 1 to get the value of J

D + 3 = J                         Equation 1

9 + 3 = J                         Substitution

12 = J                             Simplify