Answer:
d = 7.4 cm is the distance between the two cities on the map.
Step-by-step explanation:
Let d = the distance measured on the map in centimeters (cm) between any two locations and let D be the actual distance in kilometers (km) between these same two locations.
Since the scale on the map is 1 cm = 45 km, then the ratio of the distance on the map to the actual distance is equal to 1cm/45 km; therefore the quotient of any measured distance d on the map divided by the corresponding much longer actual distance D would have to maintain (equal) this same ratio; In other words, we can set up the following proportion to solve for d given the actual distance D = 333 km as follows:
1 cm/45 km = d/D
Substituting, we get:
1 cm/45 km = d/333 km
d/333 km = 1 cm/45 km
(d/333 km)(333 km) = (1 cm/45 km)(333 km)
d = (333 km/45 km)(1 cm)
d = 7.4 cm is the distance between the two cities on the map.
Check:
1 cm/45 cm = d/333 km
1 cm/45 cm = 7.4 cm/333 km
1 cm/45 cm = 1 cm/45 km (Therefore, the distance ratio of the map has been maintained
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