Math Problems Leading to Equations

In this section, we will solve math problems by forming equations and reasoning through them.

Example Problem

The sum of three consecutive numbers is 219. What are the numbers?

Solution:

Let the first number be \( x \). Then the next two numbers are \( (x + 1) \) and \( (x + 2) \).

\( x + (x + 1) + (x + 2) = 219 \)

\( 3x + 3 = 219 \)

\( 3x = 216 \)

\( x = 72 \)

So the three numbers are 72, 73, and 74. (Check: \( 72 + 73 + 74 = 219 \))

Isosceles Triangle Example

Find the value of \( x \) and the perimeter of this isosceles triangle.

As the triangle is isosceles:

\( 4x + 2 = 7x – 4 \)

\( 2 + 4 = 7x – 4x \)

\( 6 = 3x \)

\( x = 2 \)

Check: \( 4 \times 2 + 2 = 7 \times 2 – 4 = 10 \)

The sides are 10, 10, and 6 so the perimeter is 26.

Practice Exercises