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Designer Dolls, Inc. found that the number N of dolls sold varies directly with their advertising budget A and inversely with the price P of each doll. The company sold 5200 dolls when $26,000 was spent on advertising and the price of a doll was set at $30. Determine the number of dolls sold when the amount spent on advertising is increased to $52,000. Round to the nearest whole number.. . A. 5,200 dolls. . B. 1,723 dolls. . C. 3,447 dolls. . D. 10,400 dolls

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meerkat18
The correct answer among all the other choices is D. 10,400 dolls. This is the number of dolls sold when the amount spent on advertising is increased to $52,000. Thank you for posting your question. I hope that this answer helped you. Let me know if you need more help. 
TaeKwonDoIsDead

Answer:

D


Step-by-step explanation:

Direct Variation takes the form  [tex]A = kB[/tex]  

Inverse Variation takes the form  [tex]A=k(\frac{1}{B})[/tex]

  • Where A and B are the 2 variables associated and k is the proportionality constant.

Since number of dolls [N] varies directly with advertising budget [A], in our equation, A should go in the numerator and since number of dolls [N] varies inversely with price of dolls [P], P should go in the denominator.

Thus we can write our equation as:

[tex]N=k(\frac{A}{P})[/tex]

Solving this equation for k given the information "The company sold 5200 dolls when $26,000 was spent on advertising and the price of a doll was set at $30":

[tex]N=k(\frac{A}{P})\\5200=k(\frac{26,000}{30})\\5200=k(866.67)\\k=\frac{5200}{866.67}=5.99[/tex]

Rounding [tex]k=5.99[/tex] to [tex]k=6[/tex]


Now, given that we want to find the number of dolls [N] when [tex]A=52,000[/tex]  and  [tex]P=30[/tex] , we have:

[tex]N=(6)(\frac{52,000}{30})\\N=10,400[/tex] dolls

Answer choice D is correct.


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