When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5 the remainder is 4.The remainder is z when x+y is divided by 5. Find the value of (2z - 5)/3.

Guest Jul 6, 2020

#1**+3 **

**When a natural number x is divided by 5, the remainder is 2. When a natural number y is divided by 5, the remainder is 4. The remainder is z when x+y is divided by 5. Find the value of \(\dfrac{2z - 5}{3}\).**

\(\begin{array}{|lrcll|} \hline & x & \equiv & 2\pmod{5} \qquad (1) \\ & y & \equiv & 4\pmod{5} \qquad (2) \\ \hline (1)+(2): & x+y & \equiv & 2+4\pmod{5} \\ & x+y & \equiv & 6 \pmod{5} \\ & x+y & \equiv & 6-5 \pmod{5} \\ & x+y & \equiv & {\color{red}1} \pmod{5} \\ \hline & z &=& 1 \\\\ & && \mathbf{\dfrac{2z - 5}{3}} \\\\ & &=& \dfrac{2*1 - 5}{3} \\\\ & &=& \dfrac{-3}{3} \\\\ & &=& \mathbf{-1} \\ \hline \end{array}\)

heureka Jul 6, 2020