Designer Dolls, Inc. found that the number of dolls sold, N, varies directly as their advertising budget, A, and inversely as the price of each doll, P. Designer Dolls, Inc. sold 12,000 dolls when $50,000 was spent on advertising and the price of the doll was set at $50. Determine the number of dolls sold when the amount spent on advertising is increased to $65,000.
a.
15,600
b.
1,300
c.
2,880
d.
15,120
N = kA/P
That mean that
NP/A = k, a constant
So, you want to find N such that
50N/65 = 50*12/50
where we have expressed A and N in thousands
To solve this problem, we need to use the given information and apply the concept of direct and inverse variation.
Let's start by writing the given information as a direct and inverse variation equation:
N = (k * A) / P
Where:
N = number of dolls sold
A = advertising budget
P = price of each doll
k = constant of variation
From the question, we are given that when $50,000 was spent on advertising and the price of the doll was $50,000, 12,000 dolls were sold. We can use these values to find the constant of variation, k.
12,000 = (k * 50,000) / 50
To solve for k, we can cross-multiply and then divide:
12,000 * 50 = k * 50,000
600,000 = k * 50,000
k = 600,000 / 50,000
k = 12
Now that we have found the value of k, we can use it to find the number of dolls sold when the advertising budget is increased to $65,000.
N = (12 * 65,000) / 50
N = 780,000 / 50
N = 15,600
Therefore, the number of dolls sold when the amount spent on advertising is increased to $65,000 is 15,600.
So, the correct answer is option a. 15,600.