Mathematics

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?

1 Answer

  • 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.