Question

Let H represent the height of the Colossus roller coaster. Explain why H - 13= 184 and h-34=163 are equivalent equations. Then explain the meaning of the solution.

Answer 1

Explanation:

The two equations are $H-13=184$ and $H-34=163$

To determine why the two equations are equivalent, let us solve the equation.

Consider solving the equation $H-13=184$, we get,

Adding 13 on both sides, we get,

$H=197$

Consider solving the equation $H-34=163$, we get,

Adding 37 on both sides, we get,

$H=197$

Thus, when solving both the equations, the value of H is equal.

Since, the value of H is equal, the equations $H-13=184$ and $H-34=163$ are equivalent equations.

The meaning of the solution:

A value of a variable which makes the equation true is called a solution.

Here the value of the variable H is 197. Let us substitute the value in the equations $H-13=184$ and $H-34=163$ to determine whether it makes the equation true.

Let us substitute $H=197$ in $H-13=184$, we get,

$197-13=187$

       $187=187$

Hence, $H=197$ is true solution.

Also, let us substitute $H=197$ in $H-34=163$, we get,

$197-34=163$

       $187=187$

Hence, $H=197$ is true solution.