Math please, please help

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Charlotte is planning a trip from her house in City A to the State Fair in City B. She uses 2 maps, each with a different scale & places them together so that they show her route. First map's scale is
2 3/4 inches with 3/4 inch equaling 30 miles. Second map's scale is 3 7/8 inches with 1/2 inch equaling 10 miles.

The answer I got is 210 miles total...but it took me forever to figure it out. I know there's a simpler way.

  • Math please, please help -

    All your numbers can be changed to nice decimals
    3/4 = .75 ,
    2 3/4 = 2.75
    3 7/8 = 3.875

    map1:
    .75 inch ---> 30 miles
    1 inch -----> 30/.75 = 40
    2.75 inches--> 40(2.75) or 110 miles

    map2:
    .5 inches -----> 10 miles
    1 inches ------> 10/.5 = 20 miles
    3.875 --------> 20(3.875) or 77.5 miles

    You don't make it clear how the two maps are used. Does she use map1 for some part of the trip and then continue with map2 with the last leg of the trip?
    If so, then just add up 77.5+110 = 187.5 miles

    How did you get 210 ??

    BTW, the method I used is sometimes called the unit rate method, that is, you find how much for 1 unit of whatever.

    e.g. 6 oranges cost $4.32, how much would you pay for 4 oranges ?
    6 oranges cost 4.32
    1 orange costs 4.32/6 = .72
    4 oranges cost 4(.72) = $2.88

    For many people using a simple ratio is often faster, but folks get confused about setting up the 2 fractions
    x/4.32 = 4/6
    cross-multiply
    6x = 4(4.32)
    x = 4(4.32)/6 = 2.88
    (notice the actual calculations are the same)

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