Q67. - Algebra 2

Question

For the exercise 67, define a variable, write an equation, and solve the problem.

 

FAMILY  Chun-Wei’s mother is 8 more than twice his age. His father is three years older than his mother is. If all three family members have lived 94 years, how old is each family member?

Step-by-Step Solution

Answer

The required age of Chun-Wei, Chun-Wei’s mother and Chun-Wei’s father is $41.5$, 91 and 94.

Step 1- Define the required variable

Consider x be the age of Chun-Wei. 

Step 2 – Form the equation

Take the variable and form the equation by using that the two times of Chun-Wei’s age plus 8 plus 3 is equal to the total living years.

$2x+8+3=94$

Step 3- Solve the equation for x

Write the obtained equation in simplified form.

$2x+11=94$

Perform subtraction of 11 from both sides of the equation.

$\begin{array}{c}2x+11-11=94-11\\ 2x=83\end{array}$

Perform division of 2 on both sides of the equation.

 $\begin{array}{c}\frac{2x}{2}=\frac{83}{2}\\ x=41.5\end{array}$

Step 4- Determine the age of Chun-Wei’s parents

Determine the age of Chun-Wei’s mother by performing the addition of 8 to the double of Chun-Wei’s age.

$\begin{array}{c}2\left(41.5\right)+8=83+8\\ =91\end{array}$

Determine the age of Chun-Wei’s father by performing the addition of 3 to the age of Chun-Wei’s mother. 

$91+3=94$

Step 5- Perform the checking

As the age of Chun-Wei’s father is equal to the total lived years then obtained ages are correct because the highest age in the family is the age of Chun-Wei’s father.