Question

PLEASE HELP The ratio of boots to sandals in a shoe store is 8:3. If there are 245 more boots that sandals in the store, how many boots are there?

Answer 1

X - the number of boots
y - the number of sandals

The ratio of boots to sandals is 8:3.
$\frac{x}{y}=\frac{8}{3} \\ 8y=3x \\ y=\frac{3}{8}x$

There are 245 more boots than sandals.
$y+245=x \\ y=x-245 \\ \\ y=y \\ \frac{3}{8}x=x-245 \\ \frac{3}{8}x-x=-245 \\ \frac{3}{8}x-\frac{8}{8}x=-245 \\ -\frac{5}{8}x=-245 \\ x=-245 \times (-\frac{8}{5}) \\ x=49 \times 8 \\ x=392$

There are 392 boots.