Răspuns :
4kg capsuni......5kg cirese..... costa 69 lei/×3
3kg capsuni.......4kg cirese....costa 54 lei/×4
12kg capsuni.....15kg cirese....costa 207 lei
12 kg capsuni...16kg cirese...costa 216 lei
16-15=1
216-207=9
9÷1=9lei(un kg capsuni)
9×15=135
207-135=72lei(un kg cirese)
3kg capsuni.......4kg cirese....costa 54 lei/×4
12kg capsuni.....15kg cirese....costa 207 lei
12 kg capsuni...16kg cirese...costa 216 lei
16-15=1
216-207=9
9÷1=9lei(un kg capsuni)
9×15=135
207-135=72lei(un kg cirese)
[tex]a - capsuni[/tex]
[tex]b - cirese[/tex]
[tex]\left\{\begin{matrix} 4a + 5b = 69 \: | \times 4 & & \\
3a + 4b = 54 \: | \times ( - 5) & &
\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
16a + 20b = 276 & & \\
- 15a - 20b = - 270 & &
\end{matrix}\right.[/tex]
[tex]16a -15a + 20b - 20b = 276 - 270[/tex]
[tex]a = 6[/tex]
[tex]4a + 5b = 69[/tex]
[tex]4 \times 6 + 5b = 69[/tex]
[tex]24 + 5b = 69[/tex]
[tex]5b = 69 - 24[/tex]
[tex]5b = 45[/tex]
[tex]b=45:5[/tex]
[tex]b=9[/tex]
[tex]b - cirese[/tex]
[tex]\left\{\begin{matrix} 4a + 5b = 69 \: | \times 4 & & \\
3a + 4b = 54 \: | \times ( - 5) & &
\end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
16a + 20b = 276 & & \\
- 15a - 20b = - 270 & &
\end{matrix}\right.[/tex]
[tex]16a -15a + 20b - 20b = 276 - 270[/tex]
[tex]a = 6[/tex]
[tex]4a + 5b = 69[/tex]
[tex]4 \times 6 + 5b = 69[/tex]
[tex]24 + 5b = 69[/tex]
[tex]5b = 69 - 24[/tex]
[tex]5b = 45[/tex]
[tex]b=45:5[/tex]
[tex]b=9[/tex]