System of Equations Problem

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $270 and first class tickets for $980. She used her total budget for airfare for the trip, which was $4830. How many first class tickets did she buy? How many coach tickets did she buy?

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absor201 absor201 · Answer 1 · 2020-01-31T08:42:19+01:00

Sarah bought 3 first class tickets and 7 coach tickets.

Step-by-step explanation:

Given,

Number of people = 10

Total amount spent on tickets = $4830

Cost of each coach ticket = $270

Cost of each first class ticket = $980

Let,

x be the number of coach tickets

y be the number of first class tickets

According to given statement;

x+y=10 Eqn 1

270x+980y=4830 Eqn 2

Multiplying Eqn 1 by 270

[tex]270(x+y=10)\\270x+270y=2700\ \ \ Eqn\ 3\\[/tex]

Subtracting Eqn 3 from Eqn 2

[tex](270x+980y)-(270x+270y)=4830-2700\\270x+980y-270x-270y=2130\\710y=2130[/tex]

Dividing both sides by 710

[tex]\frac{710y}{710}=\frac{2130}{710}\\y=3[/tex]

Putting y=3 in Eqn 1

[tex]x+3=10\\x=10-3\\x=7[/tex]

Sarah bought 3 first class tickets and 7 coach tickets.

Keywords: linear equation, elimination method

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