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.

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.

A. 877 dolls
B. 710 dolls
C. 2,224 dolls
D. 1,800 dolls

Answer 1

1. B

2.A(y=16/x)
3.C(nc=100)
4.C(10)
5.C(2,224 dolls)

Answer 2

42000/34000 X 1800 = 42/34 X 1800 = 2223.5 or 2224 dolls

Answer 3

Hall is 💯

Answer 4

Hall is right in 2022

Answer 5

Hall is right in February of 2022 :)

Thanks Hall

Answer 6

To solve this problem, we can use the direct and inverse variation formulas.

Given:
N (number of dolls) varies directly with the advertising budget A.
N varies inversely with the price of each doll P.

We are also given some data points:
- When $34,000 was spent on advertising (A), 1,800 dolls (N) were sold.
- The price of each doll (P) was set at $25.00.

First, let's express the direct and inverse variation formulas:

Direct Variation: N = kA
Inverse Variation: N = k/P

Next, we need to find the value of constant k in each case.

Direct Variation:
We can use the data point where $34,000 was spent on advertising, and 1,800 dolls were sold.
Plugging these values into the direct variation formula: 1,800 = k * 34,000
Solving for k: k = 1,800 / 34,000 ≈ 0.053

Inverse Variation:
Using the data point where the price of each doll was set at $25.00, and 1,800 dolls were sold.
Plugging these values into the inverse variation formula: 1,800 = k / 25
Solving for k: k = 1,800 * 25 = 45,000

Now, we can use the values of k to determine the new number of dolls sold when $42,000 is spent on advertising.

Using the direct variation formula: N = kA
Plugging in the new advertising budget, A = $42,000, and k ≈ 0.053: N = 0.053 * 42,000
N = 2,226

Therefore, the number of dolls sold when the advertising budget is increased to $42,000 is approximately 2,226 dolls.
Rounded to the nearest whole number, the answer is C. 2,224 dolls.

Answer 7

N = k(A)(1/P)

for the given:
1800 = k(34000)(1/25)

solve for k, then you have the actual equation.
Plug in A=42000, P = 25