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Chapter 2: Problem 4

For each of the following conversions, write an equation of the form \(a x=b .\) Use letters of your own choosing. Determine the unknown in each equation to answer each question. a. There are 5280 feet in one mile. How many feet are in 4 miles? b. There are 16 ounces in 1 pound. How many pounds are in 832 ounces? c. There are 100 centimeters in 1 meter. How many centimeters are in 49 meters? d. Computers store data in units called bits and bytes. There are 8 bits in 1 byte. How many bytes are in 4272 bits?

Short Answer

Expert verified
How many pounds are in 832 ounces? How many centimeters are in 49 meters? How many bytes are in 4272 bits? Answer: There are 21,120 feet in 4 miles, 52 pounds in 832 ounces, 4900 centimeters in 49 meters, and 534 bytes in 4272 bits.

Step by step solution

01

a. Conversion between Feet and Miles

We need to convert miles into feet. We are given that there are 5280 feet in one mile. Using the information, we can write an equation in the form \(a x = b\), where \(x\) is the number of feet in 4 miles. Therefore, we can write the equation as: \(5280 \times x = 4y\). Now, we can find the unknown variable \(y\) by solving the equation.
02

a. Solution

To find the number of feet (y) in 4 miles (given x = 4), substitute the value of x in the equation: \(5280 \times 4 = y\) \(21120 = y\) The number of feet in 4 miles is 21,120 feet.
03

b. Conversion between Ounces and Pounds

We need to convert ounces into pounds. We are given that there are 16 ounces in one pound. Therefore, we can write an equation in the form \(a x=b\), where the x is the number of pounds in 832 ounces. Therefore, we can write the equation as: \(16x=832\). Now, we can find the unknown variable \(x\) by solving the equation.
04

b. Solution

To find the number of pounds (x) in 832 ounces, solve the equation: \(16x = 832\) \(x = \frac{832}{16}\) \(x = 52\) There are 52 pounds in 832 ounces.
05

c. Conversion between Centimeters and Meters

We need to convert meters into centimeters. We are given that there are 100 centimeters in one meter. Therefore, we can write an equation in the form \(a x=b\), where the x is the number of centimeters in 49 meters. Therefore, we can write the equation as: \(100x=49y\). Now, we can find the unknown variable \(y\) by solving the equation.
06

c. Solution

To find the number of centimeters (y) in 49 meters (given x = 49), substitute the value of x in the equation: \(100 \times 49 = y\) \(4900 = y\) There are 4900 centimeters in 49 meters.
07

d. Conversion between Bits and Bytes

We need to convert bits into bytes. We are given that there are 8 bits in one byte. Therefore, we can write an equation in the form \(a x=b\), where the x is the number of bytes in 4272 bits. Therefore, we can write the equation as: \(8x=4272\). Now, we can find the unknown variable \(x\) by solving the equation.
08

d. Solution

To find the number of bytes (x) in 4272 bits, solve the equation: \(8x = 4272\) \(x = \frac{4272}{8}\) \(x = 534\) There are 534 bytes in 4272 bits.

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