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Two wizards make boxes with secret compartments to sell at the magic convention. Fred plans to make 160 boxes by the start of the convention. Georgiana plans to make 25% fewer in the same amount of time. Fred makes 10 more boxes each day than Georgiana, and finishes his job 2 days before the convention. How many boxes does Georgiana make each day if she needs two extra days after the convention starts to complete her job?

Respuesta :

Answer:

10

Step-by-step explanation:

No i dont think I wil

Fred finishes his job 2 days before and makes 10 boxes than Georgiana

each day, the number of boxes Georgiana makes each day are 10 boxes.

Which method can be used to find the boxes made?

The number of boxes Fred plans to make = 160 boxes

Number of boxes Georgiana plans to make = 25% fewer than Fred

Number of boxes Fred makes each day = 10 more than the number of boxes Georgina makes

Number of days before the convention Fred finishes his job = 2 days before the convention

Number of days after the convention Georgina completes her job = 2 days after the convention starts

Let x represent the number of boxes Fred makes per day and let y

represent the number it takes Fred to complete his job, we have the

following equations;

x × y = 160

(x - 10) × (y + 4) = 0.75 × 160 = 120

Which gives;

[tex]\mathbf{(x - 10) \times \left(\dfrac{160}{x} +4 \right)} = 120[/tex]

4·x² + 120·x - 1600 = 120·x

4·x² + 120·x - 120·x = 1600

4·x² = 1600

x = √(1600 ÷ 4) = 20

The number of boxes Fred makes each day, x = 20 boxes

Number of days Fred takes, y = 160 ÷ 20 = 8

  • The number of boxes Georgina makes each day = 20 - 10 = 10

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