Q24. - Algebra 1

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.

Step-by-Step Solution

Answer

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

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.