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 and the price of a doll is still $30. Round to the nearest whole number.

Answer 1

The number of dolls sold is 10,400.

Explanation:

The number (N) of dolls sold varies directly as their advertising budget (A) and inversely with the price (P) of each doll.

Mathematically, the statement above is represented as:

N = kA/P

k is the proportionality constant.

k = NP/A = 5,200 × 30/26,000 = 6

When A = $52,000 and P = $30

N = kA/P = 6 × 52,000/30 = 10,400 dolls

Answer 2

Given information:

Number of dolls = N₁ = 5200

Advertising cost = A₁ = $26000

Advertising cost = A₂ = $52000

Cost of each doll = P = $30

Required Information:

Number of dolls = N₂ = ?

Answer:

Number of dolls = N₂ = 10400

Explanation:

The number of dolls sold are directly proportional to the advertising expenses.

N ∝ A

The number of dolls sold are inversely proportional to the cost of each doll.

N ∝ 1/P

N = kA/P

Where k is the constant of proportionality.

Firstly, determine the constant k

k = PN₁/A₁

k = (30*5200)/26000

k ≈ 6

Now we can find the revised number of dolls at new advertising cost.

N₂ = kA₂/P

N₂ = (6*52000)/30

N₂ = 10400 dolls

As expected since the advertising cost and number of dolls were directly proportional, an increase in advertising cost would cause increase in the number of dolls .