Chapter 8.5, Problem 34STP

To determine

The average attendance

Answer to Problem 34STP

The average attendance is $x=2$ .

Option B is correct

Explanation of Solution

Given:

Yesterday, the math club had 1 less than 3 times their average attendance. Last week they had 3 more than their average attendance

Concept Used:

• 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 the average attendance, let x be the average attendance of math club

Given that the attendance yesterday was $3x-1$ and the attendance last week was $x+3$

If attendances were the same then we equate the both equation

Thus, the equation is $3x-1=x+3$

In order to solve the equation $3x-1=x+3$ first subtract both sides by $x$ and then add both sides by $1$ and then divide both sides by $2$ and then simplify further as below:

  $\begin{array}{c}3x-1=x+3\\ 3x-1-x=x+3-x\\ 2x-1=3\\ 2x-1+1=3+1\\ 2x=4\\ \frac{2x}{2}=\frac{4}{2}\\ x=2\\ \Rightarrow x=-5\end{array}$

Thus, the average attendance is $x=2$ .

Option B is correct