Question

The number of phone calls between two​ cities, N, during a given time period varies directly as the populations p 1 and p 2 of the two cities and inversely as the​ distance, d, between them. If 18 comma 000 calls are made between two cities 310 miles apart and the populations of the cities are 15 comma 500 and 180 comma 000​, how many calls are made between two cities with populations of 100 comma 000 and 160 comma 000 that are 435 miles​ apart?

Answer 1

Answer:

∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.

Step-by-step explanation:

Given that,

The number of phone calls between two cities (N )

• directly proportional as the value of populations $p_1$  and $p_2$  of two cities.
• Inversely varies as the magnitude of distance (d).

$N\propto\frac{p_1p_2}{d}$

$N=k.\frac{p_1p_2}{d}$

Given that,

N=18,000, d=310 miles,  $p_1$=15,500 and $p_2$=180,000

$18,000=k.\frac{15,500\times 180,000}{310}$

$\Rightarrow k=\frac{18,000\times310}{15,500\times 180,000}$

$\Rightarrow k=\frac{31}{15,500}$

Now,

N=? , d=435 miles,  $p_1$=100,500 and $p_2$=160,000

$N=\frac{31}{15,500}.\frac{100,000\times 160,000}{435}$

$\Rightarrow N\approx 73,563$

∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.