word problems

Question

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 9 people took the trip. she was able to purchase coach tickets for $240 and first class tickets for $910. she used her total budget for airfare for the trip, which was $6180. how many first class tickets did she buy? how many coach tickets did she buy?

 

Answer 1

Hi Bianca, set up two equation in x and y and then solve for either the x or y.

 

Equation 1:

 

x + y = 9, this represents the number of people and / or it represents the number of each type of ticket.

 

Equation 2:

 

x * 240 + y * 910 = 6180, this represents the money spent of each type of ticket.

 

Solve:

 

      x +      y =      9

240x + 910y = 6180

 

multiply the first equation by -240 and then subtract the two equations to eliminate the x variable.

 

-240x    -    240y   =   -2160

 240x    +   910y   =    6180

--------------------------------

0x         +  670y    =    4020

 

Divide both sides by 670 giving:

 

y = 6, or 6 first class tickets were purchased.

 

Substitute for y in equation 1 to find the value for x.

 

x + 6 = 9

 

Subtract 6 from both sides gives:

 

x = 3

 

Solution: Sarah purchased 3 coach tickets and 6 first class tickets.

 

Check:

 

substitute for x and y in the second equation.

 

3 * 240 + 6 * 910 = 6180

 

720 + 5460 = 6180

 

6180 = 6180, values check.

 

Questions?