NMMRUS 3 Loesung

Eierspeise

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Wir nennen die Anzahl an Eieren, die der Koch nach Hause getragen hat und nach denen gefragt wird x. Ein Duzent Eier koster p Cent (ein Duzent = 12 Stück).

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x-2) \cdot {p \over 12} = 12}

Das sind die Eier, die der Koch tatsächlich bezahlt hat (x-2) - zum ursprünglichen Preis (p). p wird durch 12 dividiert, weil p der Preis für ein Duzent Eier ist.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x \cdot {{p - 1} \over 12} = 12}

Das sind die Eier, für die der Koch den Preis zurückrechnet - wie erwähnt p-1.

Weil mir das "durch 12" nicht gefällt, werden beide Gleichungen mit 12 multipliziert und dann gleich gesetzt:

$(x-2)\cdot p=144$
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x \cdot (p-1) = 144}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (x-2) \cdot p = x \cdot (p-1)}

Die letzte Gleichung wird ausmultipliziert.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle xp - 2p = xp - x}

Auf beiden Seiten kann man xp subtrahieren.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2p = -x }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2p=x}

Die letze Erkenntnis kann man in eine der Gleichungen von vorher einsetzen (x=2p).

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (2p-2) \cdot p = 144}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2p^2-2p=144}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p^2-p=72}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p^2-p-72=0}

Jetzt heißt es Quadratische Gleichungen auflösen ;-)

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{1,2} = {1 \over 2 } {+ \over -} \sqrt{{1 \over 4} + 72}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{1,2} = {1 \over 2 } {+ \over -} \sqrt{{1 + 4\cdot72} \over 4}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle p_{1,2} = {1 \over 2 } {+ \over -} {\sqrt{1+288}} \over 2}}