Answer
40, 96
Work Step by Step
Let one number be $x$ and the other number be $y$.
If 4 times the larger number minus the smaller number is equal to 64, then $4y-x=64$. This is the first of the two simultaneous equations.
Also, twice the larger number plus the smaller number is 176.
Therefore, $x+2y=176$. We write the equation $x+2y=176$ as $x=176-2y$ to make $x$ the subject of the equation. This is the second of the two simultaneous equations.
Therefore, we now have a pair of simultaneous equations to solve. Substituting this second equation in the first equation, we obtain:
$4y-x=64$
$4y-(176-2y)=64$
$4y-176+2y=64$
$4y+2y=64+176$
$6y=240$
$y=\frac{240}{6}=40$
We now substitute the value of $y$ in the first equation to find the value of $x$,
$4y-x=64$
$4(40)-x=64$
$160-x=64$
$x=160-64$
$x=96$
Therefore, the smaller number is 40 while the larger number is 96.
