Problem Solving

Vincen wrote:Jane drives n miles to the mall. She then drives 3 miles to the bank and 2 miles to the movies. If she is now 12 miles from her starting point, what is the range of possible values for n?

A) 4≤n≤12

B) 5≤n≤12

C) 7≤n≤15

D) 7≤n≤17

E) 12≤n≤17

The OA is D.

I don't know how could I determine the range of n. I think a graph could help me. Any expert can help me?

To find out the range of possible values for n, we must find out its minimum possible and maximum possible value n.

Say SP: Starting point; Ma: Mall; B: Bank; and Mo: Movie

Case 1: Maximum possible value of n:

Going to Mall, then on the return journey, going to Bank and then following the same route to Movies.

Ma-----------------B--------------Mo-------------SP
<----------------------n miles----------------------->
<----3 miles-----><--2 miles---><--12 miles--->

=> n = 3+2+12 = 17

Case 2: Maximum possible value of n:

Going to Mall, then following the same route, going to Bank and then to Movies.

Mo-----------------B--------------Ma-------------SP
<----------------------12 miles--------------------->
<----2 miles-----><--3 miles---><--n miles--->

=> 12 = 2+3+n
=> n = 7

Thus, 7 ≤ n ≤ 17

The correct answer: D

Hope this helps!

-Jay

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