## anonymous one year ago if janet walks 1.5 km on Monday night how many cm. map shows 1;30000

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1. mathstudent55

1:30,000 means that for each 1 cm of map distance, there are 30,000 cm of real distance.

2. anonymous

okay well i'm not totally sure here but if its asking how many cm did she walk on monday night then the answer would be 150000 because theirs 100000 cm every 1 km

3. mathstudent55

$$\dfrac{real~distance}{map~distance} ~~~~~~~\dfrac{1.5~km}{x} = \dfrac{30,000~cm}{1~cm}$$

4. mathstudent55

We are looking for a map distance, so x has to be in cm. Since the denominator of the second fraction is in cm, the second denominator stays as is. We need to have the two numerators in the same units. The units don't have to be cm or km. They can be any units as long as both numerators have the same units. An easy unit to use is meters. Let's keep this same proportion, but change both numerators to meters. $$\dfrac{1.5~km \times \frac{1000~m}{1~km}}{x} = \dfrac{30,000~cm \times \frac{1~m}{100~cm}}{1~cm}$$ $$\dfrac{1500~m}{x} = \dfrac{300~m}{1~cm}$$ Now that we have the same units of real distance and the same units for map distance, we just solve the proportion. $$x = \dfrac{1500~m \times 1~cm}{300~m}$$ $$x = 5 ~cm$$

5. mathstudent55

Let's check our answer. We got 5 cm map distance. She walked 1.5 km. We get 5 cm on the map. Since the scale is 1:30,000, 1 cm on the map is 30,000 cm real distance, so 5 cm on the map = 5 * 30,000 cm real distance. 5* 30,000 = 150,000 cm $$150,000 ~cm \times \dfrac{1~m}{100~cm} \times \dfrac{1~km}{1000~m} = 1.5~km$$ We do get 1.5 km real distance from 5 cm map distance, so our answer is correct.