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 1,800 dolls when $34,000.00 was spent on advertising, and the price of a doll was set at $25.00. Determine the number of dolls sold when the amount spent on advertising is increased to $42,000.00. Round to the nearest whole number. (1 point) Responses A. 877 dolls A. 877 dolls B. 710 dolls B. 710 dolls C. 2,224 dolls C. 2,224 dolls D. 1,800 dolls

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 1,800 dolls when $34,000.00 was spent on advertising, and the price of a doll was set at $25.00. Determine the number of dolls sold when the amount spent on advertising is increased to $42,000.00. Round to the nearest whole number. (1 point) Responses A. 877 dolls A. 877 dolls B. 710 dolls B. 710 dolls C. 2,224 dolls C. 2,224 dolls D. 1,800 dolls

Answer 1

To solve this problem, we need to use the formula for direct variation:

N = k(A/P)

We can use the given information to solve for k:

1,800 = k(34,000/25)

Simplifying the right side of the equation, we get:

1,800 = k(1360)

Dividing both sides of the equation by 1360, we find:

k ≈ 1.324

To find the number of dolls sold when the advertising budget is increased to $42,000, we can use the equation again:

N = 1.324(42,000/25)

Simplifying, we get:

N ≈ 2,224

Therefore, the number of dolls sold when the amount spent on advertising is increased to $42,000 is approximately 2,224 dolls.
The correct answer is C. 2,224 dolls.