Odpowiedź:
[tex]\left\{\begin{array}{l}a=255\\b=272\end{array}\right.[/tex]
Szczegółowe wyjaśnienie:
Tworzymy i rozwiązujemy układ równań:
[tex]\left\{\begin{array}{l}a+b=527\\8\%a=7,5\%b\end{array}\right.\\\\\left\{\begin{array}{l}a+b=527\\0,08a=0,075b\ |*1000\end{array}\right.\\\\\left\{\begin{array}{l}a+b=527\\80a=75b\ |:5\end{array}\right.\\\\\left\{\begin{array}{l}a+b=527\\16a=15b\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\16*(527-b)=15b\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\8432-16b=15b\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\-16b-15b=-8432\end{array}\right.[/tex]
[tex]\left\{\begin{array}{l}a=527-b\\-31b=-8432\ |:(-31)\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\b=272\end{array}\right.\\\\\left\{\begin{array}{l}a=527-272\\b=272\end{array}\right.\\\\\left\{\begin{array}{l}a=255\\b=272\end{array}\right.[/tex]
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Odpowiedź:
[tex]\left\{\begin{array}{l}a=255\\b=272\end{array}\right.[/tex]
Szczegółowe wyjaśnienie:
Tworzymy i rozwiązujemy układ równań:
[tex]\left\{\begin{array}{l}a+b=527\\8\%a=7,5\%b\end{array}\right.\\\\\left\{\begin{array}{l}a+b=527\\0,08a=0,075b\ |*1000\end{array}\right.\\\\\left\{\begin{array}{l}a+b=527\\80a=75b\ |:5\end{array}\right.\\\\\left\{\begin{array}{l}a+b=527\\16a=15b\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\16*(527-b)=15b\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\8432-16b=15b\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\-16b-15b=-8432\end{array}\right.[/tex]
[tex]\left\{\begin{array}{l}a=527-b\\-31b=-8432\ |:(-31)\end{array}\right.\\\\\left\{\begin{array}{l}a=527-b\\b=272\end{array}\right.\\\\\left\{\begin{array}{l}a=527-272\\b=272\end{array}\right.\\\\\left\{\begin{array}{l}a=255\\b=272\end{array}\right.[/tex]