60-3+2x5; Value 35

Question

Rewrite the expression with parentheses to equal the given value.

Answer 1

With a problem like this, you should not simply find the answer, you should develop another process (another solution method) to add to your "toolbox" of solution methods.

 

Let me mention one that computers use because they are extremely fast -- it's called exhaustive enumeration.  It is sometimes hard to teach this to students because they think it is wasteful and inefficient.  Then, I tell them that in the time it took them to say that, the computer could have solved, roughly, a million of these problems.

 

For exhaustive iteration, you identify every possible position where parenthesis could appear and then calculate the result and see whether it equals 35.  For this problem, that's almost easy enough to do it by hand.

 

Another method:  "Start at the beginning ... and when you get to the end, stop ! "   (note: my very favorite quote from Alice in Wonderland).

 

Still another method:  Start with 60 and determine how you can get to 35.   (note for tutors: this is one of Stephen Covey's 7 Habits of Highly Effective People)

 

We could eliminate some possibilities:  the "x" should multiply small values; adding and subtracting are "fine tuning" after an approximate value is determined.

 

Ideas, yet?   [Not for the answer -- but, for a process !]

 

Oh, and have you considered nested parenthesis, yet??   (that seems reasonable)

 

Well,  60 - (3+2) * 5 = 35    looks promising  ( note, I use "*" for multiply)

  Be sure to check it !

Answer 2

If you're starting with 60 and you want to get to 35, you can figure that you want the value subtracted from 60 to be 25. So, how can you get 3+2x5 to equal 25? Since have a value of 5, may see to multiply 5 by 5. We can get a second value of 5 by adding 3 and 2. In order do 3 and 2 first (thinking about PEMDAS), put that operation in parens: (3+2).

 

So, 60-(3+2)5 = 35 ...

60-(5)5 ...

60-25 or 60+(-25) ...

= 35