Question

The distance between the two islands shown on the map is 210 miles. A ruler measures this distance on the map as 3.5 inches. How many miles would be represented by 1 3/4 inches on the map?

Answer 1

The 'scale' of the map is a ratio (or a fraction).

It's (length on the map) / (distance in the real world) .

Different maps have different scales, but the scale is normally the same
everywhere on the same map.  So no matter where it is on the map, or how
long the distance is on the map, the ratio is always the same number on that
map.

On this particular map in this question, the ratio is    (3.5 inches) / (210 miles) .
Any other measurement on the same map has the same ratio ... and what do
you have when you have equal ratios ??  That's right !  A proportion ! !

The other measurement has the ratio    (1.75 inches) / (X miles) ,  and THAT
fraction is equal to the other one.

(1.75) / ( X )  =  (3.5) / (210)

Cross-multiply in the proportion:  (1.75 times 210)  =  (3.5 times  X).

Can you find 'X' now ?

Hint:  Divide both sides of that equation by  3.5  .

Answer 2

$\frac{210}{3.5} = \frac{x}{1.75} \\ 3.5x=210*1.75 \\ 3.5x=367.5 \\ x=105$