5. Replace $\Delta$ with a number so that the equality holds:

$$
238+237+236+\Delta+264+263+262=16 \cdot 23+82 \cdot(35-19)-5 \cdot 16 \text {. }
$$

Each task is scored out of 10 points.

The use of a pocket calculator or any reference materials is not allowed.

## COUNTY COMPETITION IN MATHEMATICS
5. 

$$
\begin{aligned}
& 238+262=500 \\
& 237+263=500 \\
& 236+264=500
\end{aligned}
$$

The left side of the equation is $1500+\Delta$.

The right side of the equation:

$16 \cdot 23+82 \cdot(35-19)-5 \cdot 16=$

$=16 \cdot 23+82 \cdot 16-5 \cdot 16=\quad 1$ POINT

$=16 \cdot(23+82-5)=\quad 2$ POINTS

$=16 \cdot 100=\quad 2$ POINTS

$=1600 \quad 1$ POINT

In the end, $1500+\Delta=1600$ so $\Delta=100 \quad 1$ POINT $\qquad$

# COUNTY COMPETITION IN MATHEMATICS  February 15, 2013.  5th grade-solutions


#### Abstract

HERE IS ONE WAY TO SOLVE THE PROBLEM. IF THE STUDENT HAS A DIFFERENT APPROACH TO SOLVING THE PROBLEM, THE MEMBER OF THE COMMITTEE IS OBLIGED TO GRADE AND EVALUATE THAT APPROACH IN AN APPROPRIATE MANNER.