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.
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)
To find the total distance of Charlotte's trip, we need to calculate the distances using the scales provided for each map.
Let's start with the first map:
The scale is 2 3/4 inches, and 3/4 inch on the map equals 30 miles.
To find the distance on the first map, we can use the proportion:
(2 3/4 inches) / (3/4 inch) = x miles / 30 miles
First, let's convert the mixed fraction into an improper fraction:
(11/4 inches) / (3/4 inch) = x miles / 30 miles
Now, let's cross-multiply and solve for 'x':
4 * x miles = (11/4 inches) * 30 miles
4x = (11/4) * 30
4x = 330/4
4x = 82.5
Dividing both sides by 4:
x = 82.5 / 4
x = 20.625 miles
Therefore, the distance on the first map is approximately 20.625 miles.
Now, let's move on to the second map:
The scale is 3 7/8 inches, and 1/2 inch on the map equals 10 miles.
Again, let's set up a proportion to find the distance on the second map:
(3 7/8 inches) / (1/2 inch) = y miles / 10 miles
Converting the mixed fraction into an improper fraction:
(31/8 inches) / (1/2 inch) = y miles / 10 miles
Cross-multiplying:
8 * y miles = (31/8 inches) * 10 miles
8y = (31/8) * 10
8y = 310/8
8y = 38.75
Dividing both sides by 8:
y = 38.75 / 8
y = 4.84375 miles
Therefore, the distance on the second map is approximately 4.84375 miles.
To find the total distance of Charlotte's trip, we simply add the distances from both maps:
Total distance = Distance on the first map + Distance on the second map
Total distance = 20.625 miles + 4.84375 miles
Total distance = 25.46875 miles
Rounding to the nearest mile, the total distance of Charlotte's trip from City A to City B is approximately 25 miles.