Chapter 8.2, Problem 26GP

To determine

Find the number of people at a dinner that costs $131.50, the equation is $16+8.25p=131.50$ .

Answer to Problem 26GP

  $14\text{people}$

Explanation of Solution

Given:

The equation, $16+8.25p=131.50$ .

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 number of people at a dinner, solve the given equation $16+8.25p=131.50$ for the unknown variable, isolate the variable term p on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate p on left side, firstsubtract 16 from both sides and then divide both sides by 8.25 and then simplify further as shown below,

  $\begin{array}{l}16+8.25p=131.50\\ 16-16+8.25p=131.50-16\\ 8.25p=115.5\\ \frac{8.25p}{8.25}=\frac{115.5}{8.25}\\ p=14\end{array}$

So, there are 14 people at a dinner.