Chapter 8.4, Problem 32IP

To determine

How many megabyte of data does carly’s computer download in each minute.

Answer to Problem 32IP

  $7.3\text{megabyte}$

Explanation of Solution

Given:

Each minute carly’s computer uploads 1.8 megabyte of data, over a period of 15 minutes the computer uploads and downloads a total of 136.5 megabyte of data.

Concept Used:

Distributive property:

Left Distributive property: $a\left(b\pm c\right)=a\cdot b\pm a\cdot c$

Right Distributive property: $\left(a\pm b\right)c=a\cdot c\pm b\cdot c$

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to find how many megabyte of data does carly’s computer download in each minute, first adding each minute data of uploading, that is 1.8 megabyte and each minute data of downloading, that is d then multiplying it by 15 because total time of uploading and downloading is 15 and then the equation is equal to 136.5 megabyte, so the equation is as shown below:

  $15(1.8+d)=136.5$

Now, to solving the equation first using distributive property on left side of the equation and then isolate the variable term d on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate d on left side, first subtract 27 from both sides and then divide both sides by 15 and then simplify further as shown below,

  $\begin{array}{l}15(1.8+d)=136.5\\ 15\cdot 1.8+15\cdot d=136.5\\ 27+15d=136.5\\ 27-27+15d=136.5-27\\ 15d=109.5\\ \frac{15d}{15}=\frac{109.5}{15}\\ d=7.3\text{megabyte}\end{array}$

So,carly’s computer download $7.3\text{megabyte}$ of data in each minute.