It's 100, Roughly Speaking

Logic Level 1

$\large9 \ \boxed{\phantom0} \ 15 \ \boxed{\phantom0} \ 57\ \boxed{\phantom0} \ 77\ \boxed{\phantom0} \ 96 = 100$

Each box in the expression above can be replaced by the mathematical operators $+$ or $-$ . How many times was the operator $+$ used to makes the expression equal to 100?

The answer is 3.

4 solutions

Chung Kevin
May 17, 2016

Relevant wiki: Arithmetic Puzzles - Fill in the Blanks

If we replace all the boxes with the addition sign, then we will get $9+15+57+77+96 = 254 \ne 100$ . Since this number is larger than the desired value of 100, we want to convert at least one of these addition signs to a subtraction signs. If we convert one of these additions signs, then the nuemrical value that by a numerical value of twice the following number.

For example, $9\color{#D61F06} - \color{#3D99F6}{15}+57+77+96 = 9+15+57+77+96 - 2(15) = 254 - 30$ .

Let $n$ be the value(s) of number(s) that after the subtractions sign. Then

$9 \ \boxed{\phantom0} \ 15 \ \boxed{\phantom0} \ 57\ \boxed{\phantom0} \ 77\ \boxed{\phantom0} \ 96 = 100 \Rightarrow 9+15+57+77+96 - 2(n) = 100 \Rightarrow 254 - 2n =100 \Rightarrow n = \boxed{77}.$