Chapter 8.5, Problem 27IP

To determine

The lengths of the coastlines of Florida and Texas

Answer to Problem 27IP

The Texas length is $367miles$ .

Florida length is $367+983=1350miles$

Explanation of Solution

Given:

Florida’s coastline is 118 miles shorter than four times the coastline of Texas. It is also 983 miles longer than the coastline of Texas

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 given equation, let x be the length of Texas coastline. Florida’s coastline is 118 miles shorter than 4 times Texas’s coastline, so we get

  $4x-118$

Also given that Florida’s coastline is 983 miles longer than Texas, so it is $x+983$

So equate the both expression

Thus, the equation for both is $4x-118=x+983$ .

In order to solve the equation $4x-118=x+983$ first subtract both sides by $x$ and then add both sides by $118$ and then divide both sides by $3$ and then simplify further as below:

  $\begin{array}{c}4x-118=x+983\\ 4x-118-x=x+983-x\\ 3x-118=983\\ 3x-118+118=983+118\\ 3x=1101\\ \frac{3x}{3}=\frac{1101}{3}\\ x=367\end{array}$

Thus, the Texas length is $367miles$ .

Florida length is $367+983=1350miles$