Converting map scale to unit rate. How many inches are in a mile?

Question

3/10 in = 7/8 mi

My answer: multiply the numerator by 8; I would get 24/10; 24/10 is equal to 70 in; 24/35 is equal to 24/10; So my answer would be 24/10 and/or 12/35?

Answer 1

7/8 * 8/7 = 1, so
3/10 * 8/7 = 24/70 = 12/35 in/mi

or, to convert miles to inches,

1 mi * (3/10 in)/(7/8 mi) = 3/10 * 8/7 = 12/35 mi

you are correct, except for the typos.

Answer 2

Your question was:
How many inches are in a mile?

What follows in your post is a mystery to me.

1 mile
= 5280 ft
= 5280(12) inches
= 63,360 inches

Now what is your map scale ?
Are we to find that scale?
does 3/10 inch on your map represent 7/8 mile?

then 3/10 inch -----> (7/8)(63,360) inches or 55440 inches
then 1 inch -----> (55440)(10/3) or 184,800

so the scale is 1 : 184,000

(go metric !)