Question

1. to transmit information on the internet, large files are broken into packets of smaller sizes. each packet has 1,500 bytes of information. an equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information.

a. how many packets would be needed to transmit 30,000 bytes of information?
b. how much information could be transmitted in 30,000 packets?
c. each byte contains 8 bits of information. write an equation to represent the relationship between the number of packets and the number of bits.
(from unit 2, lesson 6)

Explanation:

Step1: Solve for number of packets in part a

Given $b = 1500p$, when $b = 30000$, we solve for $p$ by dividing both sides of the equation by 1500. So $p=\frac{30000}{1500}$.
$p=\frac{30000}{1500}=20$

Step2: Solve for amount of information in part b

Given $b = 1500p$, when $p = 30000$, we substitute $p$ into the equation. So $b=1500\times30000$.
$b = 1500\times30000=45000000$

Step3: Find equation for bits in part c

Since $b = 1500p$ and each byte has 8 bits, let $n$ be the number of bits. Then $n = 8b$. Substitute $b = 1500p$ into $n = 8b$, we get $n=8\times1500p=12000p$.

Answer:

a. 20
b. 45000000 bytes
c. $n = 12000p$