emily has a road trip map with a key that shows an inch on the map equals 5 miles of actual distance of a distance measured on the map is 12 inches what is the actual distance write the rule you used to find the actual distance
We know that the scale is `1/5` .
Write the scale as a unit rate.
`(1/5) = (12/x)`
where `x ` is the unknown actual distance for `12` inches.
Multiply both sides by` 5x` .
`(5x)(1)/(5) = (12/x)*(5x)`
`(5x)/(5) = (12*5x)/(x)`
Cancel out common factor on top and bottom.
`1x = 60`
Isolate the x on left side, divide both side by 1.
`x = 60`
Therefore, the actual distance for 12 inches is 60 miles.
That is it!
One way to think about this problem is to think of the 1 inch on the page to be "equal" to the 5 miles in real life, because that is what scale representation means in an abstract manner. Of course, 1 inch and 5 miles are very different in real life, but for the purposes of the problem, it is fine to consider them equal for the time being.
In that case, we have the equation: 1 inch = 5 miles
Now, the problem is asking how many miles is represented by (is equal to) 12 inches. TO do this, think of what multiplier is necessary to change the 1 inch into 12 inches. Since we are multiplying by 12 on the left hand side, we have to multiply by 12 as well on the right hand side to maintain equality. Therefore, we now have the new equality: 12 inches = 60 miles.