Pat wrote a strange example on the board:

$$
550+460+359+340=2012.
$$

Mat wanted to correct it, so he searched for an unknown number that he could add to each of the five given numbers to make the example numerically correct. What was this number?

(L. Hozová)

Hint. How many numbers will Mat add to the left and how many to the right side of the equation?
The sum of four numbers on the left side of the equation is $550+460+359+340=1709$; this is a number $2012-1709$ = 303 smaller than the number on the right side of the equation. To the left side, we add

Mato's number four times, and to the right side only once. The difference of 303 between both sides must therefore be balanced by three of Mato's numbers. The sought number is therefore 303:3=101.

Note. For better clarity, we also provide a check of the previous result: After adding on the left side, we get

$$
(550+101)+(460+101)+(359+101)+(340+101)=651+561+460+441=2113
$$

on the right side, we get

$$
2012+101=2113
$$

We see that the number 101 meets the requirements. At the same time, a suitable illustration on a balance scale is offered here.

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