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The difference between two numbers is 16. Five times the smaller is the same as 8 less than twice the larger. Find the numbers

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naǫ
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.
konrad509
[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]
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