Question

If a picnic area is located at the midpoint between Sacramento and Oakland, find the distance to the picnic area from the road sign.

Roseville 5
Sacramento 23
Oakland 110

Answer 1

First, think this through. If you are 23 miles from Sacramento, and 110 miles from Oakland (I am assuming it is miles since you didn't specify *cough cough*) then the two cities are 133 miles apart (also assuming you are in between them)

`23miles + 110miles = 133miles`
so, we use the midpoint formula to find our position

`(distance)/( 2)`
and get 66.5 miles from both Sacramento and Oakland.

Next, we already know the sign is 23 miles away from Sacramento so we can use that distance and our position to figure out how far away the sign is. We use absolute values because distance is always positive.

`|our \: position - distance \: of \: sign|`

so we get

`|66.5miles - 23miles| = 43.5miles`
to double check, use the sign's distance from Oakland.

`|66.5miles - 110miles| = 43.5miles`
so, we are 43.5 miles from the sign!

hope this helps