Chapter 1, Problem 34CR

To determine

How old are Yanira, Tim, and Hannah.

Answer to Problem 34CR

  $\begin{array}{l}\text{Hannah }=5\text{years}\\ \text{Yanira }=\text{10years}\\ \text{Tim }=\text{7years}\end{array}$

Explanation of Solution

Given information:

Yanira is 3 years older than Tim and twice as old as Hannah. Tim is 2 years older than Hannah.

CONCEPT USED:

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find the age of Yanira, Tim, and Hannah,

let the age of Hannah be h ……equation 1.

Given that Yanira is twice as old as Hannah, that is

Yanira’s age is 2h………equation 2.

Tim is 2 years older than Hannah, that is

Tim’s age is h+2……equation 3.

Also, Yarina is 3 years older than Tim, that is

Yarina’s age is h+2+3……equation 4.

Now, equating the age of Yarina from equation 2 and 4

  $\begin{array}{l}2h=h+2+3\\ 2h-h=h-h+5\\ h=5\end{array}$

Now solving the equation 1,2 and 3 to get the age of Tim and Hannah

Age of Yarina is

  $\begin{array}{l}2h=2\times 5\\ =10\end{array}$

The age of Hannah is h that is

  $h=5$

and the age of Tim is

  $\begin{array}{l}h+2\\ =5+2\\ =7\end{array}$

So, the age of Yarina is 10 years , the age of Tim is 7 years, and the age of Hannah is 5 years.