Determine if the given rates are equivalent.
9in/57 miles = 6 in/38 miles
If 9 inches = 57 miles, then 1 inch equals 6 1/3 miles.
If 6 inches = 38 miles, then 1 inch equals 6 1/3 miles.
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To determine if the given rates are equivalent, we need to check if the ratios of the two rates are equal.
The first rate is 9 inches for every 57 miles, which can be written as 9 in/57 miles.
The second rate is 6 inches for every 38 miles, which can be written as 6 in/38 miles.
To compare these rates, we can set up a proportion by equating the ratios:
9 in / 57 miles = 6 in / 38 miles
Cross multiplying, we get:
9 in * 38 miles = 57 miles * 6 in
342 in * miles = 342 in * miles
Since both sides of the equation are equal, we can conclude that the given rates are indeed equivalent.