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Veronderstel dat een pakje koekjes €$x$ kost.

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Schrijf een uitdrukking neer in termen van $x$ voor de kost van elke snoepsoort (per pakje of doosje):

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Koekjes: €[[0]]

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Pralines: €[[1]]

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Lolly's: €[[2]]

Schrijf een algebraïsche uitdrukking neer, in termen van $x$ voor de totale kost van het snoepgoed dat {name} verbruikte. Doe dit in de vorm ax+b.

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€[[0]]

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Nu blijkt dat een pakje koekjes €$\\var{e1}$ kost.

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Gebruik dit om de totale kostprijs te bepalen die {name} gedurende de laatste week spendeerde aan dit snoepgoed.

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€[[0]]

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Don't use brackets

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Translation to Dutch of

\"Given a description in words of the costs of some items in terms of an unknown cost, write down an expression for the total cost of a selection of items. Then simplify the expression, and finally evaluate it at a given point.

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The word problem is about the costs of sweets in a sweet shop.\"

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Aantal pakjes koekjes

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factor als verhouding pralines t.o.v. lolly's

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Aantal doosjes pralines

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+The total spent.

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meerkost voor pralines t.o.v. koekjes

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Aantal lolly's.

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kost koekjes

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#### a)

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Volgens de gegevens wordt het aantal pakjes koekjes voorgesteld door de letter $x$.

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Een doosje pralines kost $€ \\var{d1}$ meer dan een pakje koekjes, i.e. $x+\\var{d1}$.

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Een doosje pralines kost $\\var{f1}$ maal zoveel als een doosje lolly's,

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wat impliceert dat een een doosje lolly's als kostprijs  ${\\frac{1}{\\var{f1}}}(x+\\var{d1})$ heeft.

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#### b)

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Om de totale kost te vinden, vermenigvuldig je de supra gevonden uitdrukkingen voor de kostprijs van elk snoepgoed met het aantal verbruikte pakjes of doosjes, en telt deze vervolgens op.

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Zonder vereenvoudiging betekent dit:

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\\begin{align}
\\text{Totale kost} &= \\simplify[]{{a1}x+{b1}(x+{d1}) + {c1} (1/{f1})*(x+{d1})} \\\\
&= \\simplify[]{{a1}x+{b1}(x+{d1}) + {c1/f1}*(x+{d1})}
\\text{.}
\\end{align}

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Werk de haakjes uit:

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\\begin{align}
\\simplify[]{ {a1}x + {b1}(x+{d1}) + {c1/f1}*(x+{d1})} &= \\simplify[]{ {a1}x + {b1}x + {b1}{d1} + {c1/f1}x + {c1/f1}{d1}} \\\\
&= \\simplify[] { {a1}x + {b1}x + {b1*d1} + {c1/f1}x + {c1/f1*d1} } \\text{.}
\\end{align}

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en groepeer gelijksoortige termen voor de optelling:

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\\begin{align}
\\simplify[] { {a1}x + {b1}x + {b1*d1} + {c1/f1}x + {c1/f1*d1} } &= \\simplify[]{ {a1+b1+c1/f1}x + {b1*d1+c1/f1*d1} } \\text{.}
\\end{align}

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#### c)

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Wanneer je weet dat de prijs van een pakje koekjes $€\\var{e1}$ bedraagt, kan je dit voor $x$ substitueren in bovenstaande uitdrukking uit b).

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\\begin{align}
\\text{Totale kost}&=\\var{a1+b1+c1/f1} \\cdot \\var{e1}+\\var{b1*d1+c1/f1*d1} \\\\
&=\\var{(a1+b1+c1/f1)*{e1}+b1*d1+c1/f1*d1} \\text{.}
\\end{align}

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Dus spendeerde {name} voor $€\\var{total}$ aan snoep gedurende de voorbije week.

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{name} is een grote snoeper. Je bepaalt in wat volgt de kost van alle snoep dat {name} gedurende de laatste week verorberde.

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{name} at $\\var{a1}$ pakjes koekjes, $\\var{b1}$ doosjes pralines en $\\var{c1}$ doosjes lolly's.

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Je weet dat een doosje pralines €$\\var{d1}$ meer kost dan een pakje koekjes,

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en dat een dergelijk doosje pralines $\\var{f1}$ maal zoveel kost als een doosje lolly's .

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