Chapter 5.5, Problem 34E

To determine

To find: the number of years will both pets be the same age in there respective types of years.

Answer to Problem 34E

The number of human years after which both the pets have the same age is $x=4.$

Explanation of Solution

Given:

The dog is $16$ years old in dog years.

Cat is $28$ years old in cat years.

Every one Human year dog age will $7$ and cat age will be $4$ .

Concept used:

The intersection of two straight line can be calculated as:

By equating the value of $x\text{ and }y$ which is same in the case of intersection.

Set the two equations equal to each other and solve for the point where it is intersects.

Calculation:

The objective is to find the number of human years after which both the pets have the same age.

Let $x$ be the number of human years.

Verbal model can be written as:

Age of dog $+$ dogs age in=number of cat age $+$ cat age in number of human years.

Equation:

  $16+7x=28+4x.$

Step1:

Write a system of linear equations using each side of the original equation.

Let:

  $\begin{array}{l}y=16+7x\mathrm{......}\left(i\right)\\ y=28+4x\mathrm{..........}\left(ii\right)\end{array}$

The tabular form:

$X$	$Y_1$	$Y_2$
$2$	$30$	$36$
$4$	$44$	$44$
$6$	$58$	$52$
$8$	$72$	$60$
$10$	$86$	$68$
$12$	$100$	$76$

Graph of the system:

  

It is clear from the graph both the lines intersecting at $x=4$ ,

Hence, the number of human years after which both the pets have the same age is $x=4.$