Algebra word Problem

Question

Sarah took the advertising department from her company on a round trip to meet with client. Including Sarah a total of 9 people took the trip. She was able to purchase coach tickets for $340 and first class tickets for 990$. She used her total budget which was $6310. How many first class tickets did she buy? How many coach tickets did she buy?

Answer 1

let x = no of coach tickets, y = no of first class tickets

 

Total of 9 people so 9 tickets ----> x + y = 9 (eq. 1)

Total value of 6310, 340 for a coach, and 990 for a first class -----> 340x + 990y = 6310 (eq. 2)

 

System of Linear equations

SUBSTITUTION: change eq. 1 to x = 9 - y and substitute to eq. 2, 340(9-y) + 990y = 6310; y=5; using eq 1, x=4.

OR

 

ELIMINATION: x + y = 9, multiply both sides by -340 --> -340x -340y = -3060

 

-340x - 340y = -3060

 340x + 990y = 6310

0 + 650y = 3250; y = 5, using eq 1, x = 4