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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
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]
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