x - the number of boots
y - the number of sandals
The ratio of boots to sandals is 8:3.
[tex]\frac{x}{y}=\frac{8}{3} \\
8y=3x \\
y=\frac{3}{8}x[/tex]
There are 245 more boots than sandals.
[tex]y+245=x \\
y=x-245 \\ \\
y=y \\
\frac{3}{8}x=x-245 \\
\frac{3}{8}x-x=-245 \\
\frac{3}{8}x-\frac{8}{8}x=-245 \\
-\frac{5}{8}x=-245 \\
x=-245 \times (-\frac{8}{5}) \\
x=49 \times 8 \\
x=392[/tex]
There are 392 boots.
