math problem?

Question

PROBLEM: on one flight, the airline sold twice as many economy class tickets a business class tickets. economy class costs $400 and business class costs $900. five of the economy class ticket holder remeemed a voucher and did not have to pay. the total revenue for the flight was $49,000.

a) solve the equation for n, the number of business class travelers:
900n + 400(2n - 5)= 49,000.



b) how many people traveled economy class,

Answer 1

900n + 400 (2n - 5) = 49,000
900n + 800n - 2000 = 49,000
1700n - 2000 = 49,000
Add 2000 to each side of the equation
1700n = 51,000
1700n/1700 = 51,000/1700
n = 30

800 * 30 = 24,000
24,000 + 2000 (worth of free tickets) = 26,000
26,000/400 = 65

There were 65 passengers in economy (60 paying and 5 free)

You will note that this is a trick question. Every one of the people who answered the question solved correctly for n, but the question was not how many paying passengers were there in economy, but how many passengers were there in economy. There were 65 passengers in economy.

Answer 2

a)900n + 400(2n-5) = 49000
900n + 800n - 2000 = 49000
900n + 800n = 51000
1700n = 51000
n = 30

so there are 30 business class travelers

b) the 30 business class travelers at $900 each spent $27000
there is 49000 total spent
49000-27000= 22000 spent by the economy travelers
economy tickets cost 400 each so
22000/400 = 55 - so there were 55 paying economy customers plus the 5 that used vouchers

so there were 60 economy class customers


Do the math to check your work
55 paying economy class + 5 free vouchers plus 30 business class
55*400+30*900
22000+27000=49000

Answer 3

First Start with the problem

900n+400(2n-5)=49000

Next use the distributive property.

900n+400(2n)-400(5)=49000

You''ll end up with this:

900n+800n-2000=49000

Then you'll combine like terms.

1700n-2000=49000

You will then add 2000 to cancel it out to leave the variable.

1700n-2000+2000=49000+2000

And get this:

1700n=51000

To isolate the variable, you will divide each side by 1700.

1700n 51000
--------- = ----------
1700 1700

And your answer is:

n= 30

To find the answer to the whole problem you will multiply n by 2

30*2=60

60 people traveled economy.

Answer 4

900n + 400(2n-5) = 49000
Distribute the 400
900n + 800n - 2000 = 49000
Combine 900n and 800n
1700n - 2000 = 49000
Add 2000 to each side
1700n = 51000
Divide both sides by 1700
n = 51000/1700
n = 30

b) They sold twice as many economy as business, so
2n = 2(30) = 60 economy tickets

Answer 5

900n + 400(2n - 5) = 49,000
Clear the parentheses:
900n + 800n - 2,000 = 49,000
Add 2,000 to both sides:
900n + 800n = 51,000
add the coefficients of n:
1,700n = 51,000
Divide both sides by 1,700:
n = 51,000/1,700 = 510/17 = 30

b) There were twice as many economy class as business class.
2n = 2*30 = 60

Answer 6

a) n = 30
900n + 400(2n - 5) = 49,000
900n + 800n - 2000 = 49,000
1700n = 51,000
n = 51,000/1700
n = 30

b) 2(30) = 60