# Thread: Elimination or substion word problem

1. ## Elimination or substion word problem

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 105.5 million passengers in the first six months of 1999. If Hartsfield handeled 5.5 million more passenger than O'Hare, how many were handled by each airport?

I thought it might go by elimination like this:

Hartsfield 6x+5.5=150.5
O'Hare 6x-5.5=150.5
12x=301
x=25.083 continues

I'm not sure if that is right could you please tell me if its right and if not what am doing wrong?

2. Originally Posted by nick_c
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 105.5 million passengers in the first six months of 1999. If Hartsfield handeled 5.5 million more passenger than O'Hare, how many were handled by each airport?

I thought it might go by elimination like this:

Hartsfield 6x+5.5=150.5
O'Hare 6x-5.5=150.5
12x=301
x=25.083 continues

I'm not sure if that is right could you please tell me if its right and if not what am doing wrong?
Good evening, Nick. This problem looks familiar.

Let's solve it using 2 equations...just for yuks!

Let x = #passengers handled at O'Hare
Let y = #passengers handled at Hartsfield
Let 150.5 = total passengers handled at both airports

Hartsfield handled 5.5 million more than O'hare, so

$\displaystyle y = x + 5.5$

$\displaystyle x+y=150.5$

Now, solve the system using substitution. Replace y in the second equation with x + 5.5 from the first equation.

$\displaystyle x+x+5.5=150.5$

Solve for x. Then use that value to solve for y in $\displaystyle y=x+5.5$

Can you finish?

3. Originally Posted by nick_c
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 105.5 million passengers in the first six months of 1999. If Hartsfield handeled 5.5 million more passenger than O'Hare, how many were handled by each airport?

I thought it might go by elimination like this:

Hartsfield 6x+5.5=150.5
Where did that "6" in 6x come from? From the "first six months of 1999"?
Surely you don't think that means you should multiply the number of passengers handled by by Atlanta by 6? The "6 months just tells you what time this is given over. Six everything is over that same time period, that is really irrelevant.

O'Hare 6x-5.5=150.5
12x=301
x=25.083 continues

I'm not sure if that is right could you please tell me if its right and if not what am doing wrong?
I applaud master's suggestion that you explicitely NAME your variables (which you did not do). Let x be the number of passengers at Hartsfield over that time, y the number of passengers at O'Hare over that same time (both in millions).
The total number of passengers is x+ y and we are told that is 10.5 million: x+y= 10.5

we are also told that "Hartsfield handled 5.5 million more passenger than O'Hare": x= y+ 5.5. Replace x in the first equation by y+ 5.5 and solve for y. Then use that value of y to find x.