Question

AGE Max is four years younger than his sister Brenda. The total of their ages is 16. Write and solve an equation to find their ages.

Short answer

The age of the Brenda is 10 years and the age of max is 6 years.

Step-by-step solution

Step-1. Assign variables for the Ages.

A variable is a letter or a literal used to signify an unknown quantity.

Let letter b represent the age of Brenda then it is given that Max is 4 years younger thus the age of max will be $b-4$

Step-2. Form an equation for the sum of ages.

It is given that the sum of ages of Brenda and max is 16 thus, we have:

$b+\left(b-4\right)=16$

Step-3. Simplify the equation.

We obtained the equation $b+\left(b-4\right)=16$, to simplify it, we open the brackets as shown:

$\begin{array}{l}b+\left(b-4\right)=16\\ b+b-4=16\end{array}$

Like terms are the terms having the same variables and are raised to the same index. A coefficient is the appended number in front of the variable; if no number is shown then we assume it to be 1.

Unlike terms are the terms not having the same variables and or are raised to a different index.

For example, 4 and$5x$ are unlike terms.

We can add like terms by adding their coefficients, we cannot add the unlike terms.

Now we are having the expression $b+b-4=16$, combining like terms we get:

$\begin{array}{l}b+b-4=16\\ 2b-4=16\end{array}$

Step-4. Solve the equation.

Now we are having the expression $2b-4=16$, adding 4 both sides we get:

$\begin{array}{l}2b-4+4=16+4\\ 2b=20\end{array}$

Dividing b both sides by 2 we get:

$\begin{array}{l}\frac{2b}{2}=\frac{20}{2}\\ b=10\end{array}$

Thus Brenda’s age is 10 years.

Step-5. Use the value of Brenda’s age to get the value of Max’s age.

We know that age of Max is $b-4$, plugging$b=10$ we get:

$\begin{array}{l}b-4\\ =10-4\\ =6\end{array}$

Thus, Max’s age is 6 years.