Question

The total area of town A and town B is 140,000 square miles. The area of town A is 10,000 square miles more than that of town B. Find the area land of each town.

Answer 1

Step 1: Interpret the statement provided in the question using mathematics equation

Let the area of town A be x

Let the area of town B be y

Therefore, since the sum of the two areas is 140000 sq miles, then,

$x+y=140000-----1$

Step 2: From the second statement, the area of town A (x) is 10000 sq miles more than the area of town B (y), thus, this implies

$x=y+10000-----2$

Step 3: Substitute the value of x in equation 2 into equation 1 to find the value of y

$\begin{gathered} \text{If }x=y+10000, \\ x+y=140000\text{ will be} \\ (y+10000)+y=140000 \end{gathered}$

Step 4: Collect like terms and solve for y

$\begin{gathered} y+y=140000-10000 \\ 2y=130000 \end{gathered}$

Divide both sides by the coefficient of y, which is 2

$\begin{gathered} \frac{2y}{2}=\frac{130000}{2} \\ y=65000\text{ sq. miles} \end{gathered}$

Step 5: Substitute the value of y = 65000 in equation 2 to find x

$\begin{gathered} x=y+10000 \\ x=65000+10000 \\ x=75000\text{ sq miles} \end{gathered}$

Hence, the area of town A is 75000 square miles, and the area of town B is 65000 square miles.