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Question 272632: The distance between two cities on a road map is 32 cm. The two cities are actually 150 km apart. The distance on the map between two other cities is 80 cm. How many km apart are these cities?
Found 3 solutions by mananth, ikleyn, greenestamps:
Answer by mananth(16949)   (Show Source):
You can put this solution on YOUR website! The distance between two cities on a road map is 32 cm. The two cities are actually 150 km apart. The distance on the map between two other cities is 80 cm. How many km apart are these cities?
The distance on the map is 32 cm.
which is actually 150 km.
So 1 cm on map will be 150 / 32 = 4.68 km
The distance on the map between two other cities =80 cm.
1 cm on map = 4.68 km actual
so 80 cm on the map = 80 * 4.68 km
374.40 km.
Answer by ikleyn(53742)  (Show Source):
You can put this solution on YOUR website! .
The distance between two cities on a road map is 32 cm. The two cities are actually 150 km apart.
The distance on the map between two other cities is 80 cm. How many km apart are these cities?
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I will solve the problem in other way (differently from @mananth).
At the end, I will make my comments regarding the @manant solution.
Write the proportion
 =  .
From the proportion,
x =  =  = 375 kilometers.
ANSWER. The distance between the two cities is 375 kilometers.
In my solution, calculations lead to the nice round integer number,
while manipulations in the post by @mananth produce a fractional number.
It is because the computer code, which @mananth permanently uses in his posts,
is programmed this inappropriate way. In other words, his code may produce
inappropriate numbers, so it is, actually, a dangerous tool when is used without an accurate control.
I see it from the distance of thousand miles, because, in addition to my mathematical education,
I worked as a professional computer programmer for about 40 years.
Surely, in this problem, the integer number 375 kilometers is an expected precise answer.
Answer by greenestamps(13325)  (Show Source):
You can put this solution on YOUR website!
The response from tutor @ikleyn shows one way of solving the problem using a proportion.
Here is a different way to use ratios or proportions to solve the problem, which I personally find easier to understand.
The ratio of the two distances on the map is 80:32 = 5:2, so the ratio of the actual distance is in the ratio 5:2.
ANSWER: 375 km
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