Chapter 8.5, Problem 33HP

To determine

A real-world problem and solve the equation $54+3.5x=8x$

Answer to Problem 33HP

The solution of the equation is $x=12$

Explanation of Solution

Given:

The equation $54+3.5x=8x$

Concept Used:

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 a real world problem of the equation $54+3.5x=8x$ is below

In a birthday party, person A got 8 times a number of chocolate which is equal to 54 more than 3.5 times the number of chocolates.

In order to solve the equation $54+3.5x=8x$ first subtract both sides by $3.5x$ and then divide both sides by $4.5$ and then simplify further as below:

  $\begin{array}{c}54+3.5x=8x\\ 54+3.5x-3.5x=8x-3.5x\\ 54=4.5x\\ \frac{54}{4.5}=\frac{4.5x}{4.5}\\ 12=x\\ \Rightarrow x=12\end{array}$

Thus, the solution of the equation is $x=12$