Chapter 8.4, Problem 30IP

To determine

How many rows of seats are there in business class.

Answer to Problem 30IP

l $5\text{rows}$

Explanation of Solution

Given:

An airplane has two sections, business class and economy class, In each section there are 6 seats in a row. There are 24 rows in economy class , and there are 174 seats on the plane.

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 rows of setas are there in business class, let b be the number of rows in business class, first adding both the number of rows of economy class that is 24 rows and the business row and the multiplying it by 6 number of seats in one row, is equal to 174 total number of seats in plane, so the equation is as shown below:

  $6(b+24)=174$

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

Here to isolate b on left side, first subtract 144 from both sides and then divide both sides by 6 and then simplify further as shown below,

  $\begin{array}{l}6(b+24)=174\\ 6\cdot b+6\cdot 24=174\\ 6b+144=174\\ 6b+144-144=174-144\\ 6b=30\\ \frac{6b}{6}=\frac{30}{6}\\ b=5\end{array}$

So, there are 5 rows in business class.