Q5. - Algebra 2

Question

According to the Airports Council International, the busiest airport in the world is Atlanta’s Hartsfield International Airport, and the second busiest is Chicago’s O’Hare Airport. Together they handled $150.5$ million passengers in the first six months of $1999$. If Hartsfield handled $5.5$ million more passengers than O’Hare, how many were handled by each airport?

Step-by-Step Solution

Answer

The passengers handled by Hartsfield Airport are $78$million and the passengers handled by O’Hare Airport are $72.5$million.

Step-1 – Form the equations

Let us suppose the passengers handled by Hartsfield Airport be x and the passengers handled by O’Hare Airport be y.

Now according to the question, together they handled $150.5$million passengers.

The equation so formed is below.

$x+y=150.5$

(The figures are in millions)

Consider the second statement.

Hartsfield handled $5.5$ million more passengers than O’Hare which is mathematically expressed in the equation as shown.

$x=y+5.5$

So, both the equations so formed for the given question are

$\begin{array}{c}x+y=150.5\\ x=y+5.5\end{array}$

Step-2 – Apply the substitution method of solving equations

The algebraic method of substitution involves solving the one of the two equations for one variable in terms of other variable and then substituting the expression so formed for the variable in the second equation.

Step-3 – Substitute the expression

Since, x is already expressed in terms of y so substitute $x=y+5.5$ in the equation first and solve as shown below.

$\begin{array}{c}x+y=150.5\\ y+5.5+y=150.5\\ 2y=150.5-5.5\\ 2y=145\end{array}$

Simplify it further by dividing 2 on both sides as.

$\begin{array}{c}2y=145\\ y=72.5\end{array}$

Thus, the value of y is $72.5$.

Step-4 – Substitute the value of variable

To find the value of x, substitute $y=72.5$ in the equation $x=y+5.5$ and then solve as shown.

$\begin{array}{c}x=y+5.5\\ x=72.5+5.5\\ x=78\end{array}$

Thus, the value of x is $78$.

Hence, the passengers handled by Hartsfield Airport are $78$ million and the passengers handled by O’Hare Airport are $72.5$million.