Chapter 9.7, Problem 20P

To determine

To solve: the system of equations in two variables.

Answer to Problem 20P

The age of Mary is 35 years old and age of twin brother’s are 32 years old .

Explanation of Solution

Given information:

Mary is three years older than her twin brothers. Next year, the sum of the ages of the three will be exactly 102.

Formula used:

Age problem.

Step1. The problem asks for the Bob’s age and Claire’s age now.

Step2. Let b = the Mary’s age .

Let c = the One twin brother‘s age .

Let d = the other twin’s brother age.

Step3. Use the facts of the problem to write two equations.

Step4. Solve the equations.

Calculation:

Consider ,

Let b = the Mary’s age now .

Let c = the One twin brother’s age now.

Let d = the other twin brother’s age now.

Age	Next year
Mary	$b+1$
One twin brother	$c+1$
Another twin brother	$d+1$

According to the equation,

  $=b=3+c\text{ (i)}$

Also,

  $=(b+1)+(c+1)+(d+1)=102\text{ (ii)}$

Since the age of twin brother’s will be same $c=d$ .

Substituting equation (i) in (ii)

  $\begin{array}{l}=(3+c+1)+(c+1)+(c+1)=102\\ =4+c+c+1+c+1=102\\ =2c+6+c=102\\ =3c=102-6\\ =\frac{3c}{3}=\frac{96}{3}\\ =c=32\end{array}$

Putting value of c in equation (i) we get,

  $\begin{array}{l}=b=3+c\\ =b=3+32\\ =b=35\end{array}$

Hence, the age of Mary is 35 years old and age of twin brother’s are 32 years old .