Question

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

Answer 1

Answer:

D

Step-by-step explanation:

Direct Variation takes the form  $A = kB$  

Inverse Variation takes the form  $A=k(\frac{1}{B})$

• 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:

$N=k(\frac{A}{P})$

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":

$N=k(\frac{A}{P})\\5200=k(\frac{26,000}{30})\\5200=k(866.67)\\k=\frac{5200}{866.67}=5.99$

Rounding $k=5.99$ to $k=6$

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

$N=(6)(\frac{52,000}{30})\\N=10,400$ dolls

Answer choice D is correct.

Answer 2

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.