Question

(2p) 6. Determinaţi cifrele x, y şi z pentru care scăderea 11,x9-y,3z8=z,1zy este adevărată.​

Answer 1

Răspuns:

x = 5; y = 2; z = 9

Explicație pas cu pas:

$\overline {11,x9} - \overline {y,3z8} = \overline {z,1zy} \ \Big| \ (*1000)\\\overline {11x90} - \overline {y3z8} = \overline {z1zy}$

$\begin{array}{ccccc}1&1&x&9&0\\&y&3&z&8\\-&-&-&-&-\\&z&1&z&y\end{array}$

=> y = 2

$\begin{array}{ccccc}1&1&x&9&0\\&\red{\bf2}&3&z&8\\-&-&-&-&-\\&z&1&z&\red{\bf2}\end{array}$

z poate fi 4 sau 9

pentru z = 4:

$\begin{array}{ccccc}1&1&x&9&0\\&\red{\bf2}&3&\red{\bf4}&8\\-&-&-&-&-\\&\red{\bf4}&1&\red{\bf4}&\red{\bf2}\end{array}$

=> imposibil

pentru z = 9:

$\begin{array}{ccccc}1&1&x&9&0\\&\red{\bf2}&3&\red{\bf9}&8\\-&-&-&-&-\\&\red{\bf9}&1&\red{\bf9}&\red{\bf2}\end{array}$

=> x = 5

$\begin{array}{ccccc}1&1&\red{\bf5}&9&0\\&\red{\bf2}&3&\red{\bf9}&8\\-&-&-&-&-\\&\red{\bf9}&1&\red{\bf9}&\red{\bf2}\end{array}$

=> 11,59 - 2,398 = 9,192