6. If on the scale of a map, 3⁄4 inch equals 72 miles, what is the actual distance between 2 cities that are 3 7⁄8 inches apart on the map?
0.75inch/72miles = 3.875inches/xmiles = 372miles
To find the actual distance between two cities based on a map scale, we can use a proportion.
Let's break down the information given:
On the map scale, 3/4 inch represents 72 miles.
Now, we need to set up a proportion to find the actual distance.
Let "x" represent the actual distance between the two cities.
We can set up the proportion as follows:
3/4 inch = 72 miles
3 7/8 inches = x miles
To solve this proportion, we need to cross-multiply and then solve for "x."
(3/4) / (3 7/8) = 72 / x
To simplify the fraction, we can convert the mixed number (3 7/8) to an improper fraction:
(3/4) / (31/8) = 72 / x
Next, we can invert the second fraction and multiply:
(3/4) * (8/31) = 72 / x
Multiplying the fractions on the left side gives:
24/124 = 72 / x
Now, we can cross-multiply:
24x = 72 * 124
Simplifying the right side:
24x = 8928
Finally, we can solve for "x" by dividing both sides by 24:
x = 8928 / 24
Evaluating this expression gives:
x = 372
Therefore, the actual distance between the two cities is 372 miles.