Solving a word problem with three unknowns using a linear... The sum of three numbers is 104. The first number is 6 less than the second. The third number is 3 times the second.…

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asked Nov 3, 2023 117k views

1 Answer

Shay Shmeltzer · Answer 1 · 2023-11-08T02:33:45+0000

$\begin{gathered} \text{First number=16} \\ \text{second number=22} \\ \text{Third number=66} \end{gathered}$

Let the unknown numbers be x, y, and z where

• First number = x

,

• Second number = y

,

• Third number = z

If the sum of the three numbers is 104, then;

If the first number is 6 less than the second, hence;

$\begin{gathered} x=y-6 \\ \end{gathered}$

Also, if the third number is 3 times the second, then;

Substitute equations 2 and 3 into equation 1 to reduce the variables to the function of "y" only:

$\begin{gathered} x+y+z=104 \\ (y-6)+y+3y=104 \\ y-6+4y=104 \\ 5y-6=104 \\ 5y=104+6 \\ 5y=110\rbrack \\ y=(110)/(5) \\ y=22 \end{gathered}$

Get the first number "x"

$\begin{gathered} x=y-6 \\ x=22-6 \\ x=16 \end{gathered}$

Get the third number "z"

$\begin{gathered} z=3y \\ z=3(22) \\ z=66 \end{gathered}$

Therefore the three numbers are 16, 22, and 66.