Question

1. The combined ages of three relatives is 120 years. James is three times the age of Don, and Poul is 20 years less than the age of Don. How old is each person? Variables: 111 N System: System in standard form: Augmented Matrix: James age dans age pauls age

Answer 1

Jame´s age = 84

Poul´s age=8

Don's age = 28

Explanation

Step 1

Let

x represents the age of James

y represents the age of Poul

z represents the age of Don

then

The combined ages of three relatives is 120 years.,it is

$x+y+z=120\text{ Equation(1)}$

James is three times the age of Don, it is

$\begin{gathered} x=3z\text{ Equation(2)} \\ x-3z=0 \end{gathered}$

Poul is 20 years less than the age of Don,it is

$\begin{gathered} y=z-20 \\ \end{gathered}$

$\begin{bmatrix}{1} & {1} & {1} \\ {1} & {0} & {-3} \\ {0} & {1} & {1}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {y} & {} & {} \\ {z} & {} & {}\end{bmatrix}=\begin{bmatrix}{120} & {} & {} \\ {0} & {} & {} \\ {-20} & {} & {}\end{bmatrix}$

Step 2

find x, y and z

a) replace equation (2) and (3) in equation (1)

$\begin{gathered} x+y+z=120 \\ 3z+z-20+z=120 \\ 5z=120+20 \\ z=\frac{140}{5} \\ \\ z=28 \\ \end{gathered}$

b)replace the value of z in equation (2) to find x

$\begin{gathered} x=3z \\ x=3\cdot28 \\ x=84 \end{gathered}$

c) finally, replace the value o z in equation (3) to find y

$\begin{gathered} y=z-20 \\ y=28-20 \\ y=8 \end{gathered}$

I hope this helps you