Answer :
x - the larger number
y - the smaller number
The difference between two numbers is 16.
[tex]x-y=16 \\ x=16+y[/tex]
Five times the smaller is the same as 8 less than twice the larger.
[tex]5y=2x-8 \\ 5y+8=2x \\ \frac{5}{2}y+4=x \\ \\ x=x \\ 16+y=\frac{5}{2}y+4 \\ y-\frac{5}{2}y=4-16 \\ \frac{2}{2}y-\frac{5}{2}y=-12 \\ -\frac{3}{2}y=-12 \\ y=-12 \times (-\frac{2}{3}) \\ y=4 \times 2 \\ y=8 \\ \\ x=16+y=16+8=24[/tex]
The numbers are 24 and 8.
y - the smaller number
The difference between two numbers is 16.
[tex]x-y=16 \\ x=16+y[/tex]
Five times the smaller is the same as 8 less than twice the larger.
[tex]5y=2x-8 \\ 5y+8=2x \\ \frac{5}{2}y+4=x \\ \\ x=x \\ 16+y=\frac{5}{2}y+4 \\ y-\frac{5}{2}y=4-16 \\ \frac{2}{2}y-\frac{5}{2}y=-12 \\ -\frac{3}{2}y=-12 \\ y=-12 \times (-\frac{2}{3}) \\ y=4 \times 2 \\ y=8 \\ \\ x=16+y=16+8=24[/tex]
The numbers are 24 and 8.
[tex]x,y-\text{the numbers},~x>y\\\\
x-y=16\\
5y=2x-8\\\\
x=16+y\\
5y=2x-8\\\\
5y=2(16+y)-8\\
5y=32+2y-8\\
3y=24\\
y=8\\\\
x-8=16\\
x=24\\\\
\boxed{x=24,y=8}[/tex]