Question

System of Equations Problem

Answer 1

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

$270(x+y=10)\\270x+270y=2700\ \ \ Eqn\ 3$

Subtracting Eqn 3 from Eqn 2

$(270x+980y)-(270x+270y)=4830-2700\\270x+980y-270x-270y=2130\\710y=2130$

Dividing both sides by 710

$\frac{710y}{710}=\frac{2130}{710}\\y=3$

Putting y=3 in Eqn 1

$x+3=10\\x=10-3\\x=7$

Sarah bought 3 first class tickets and 7 coach tickets.

Keywords: linear equation, elimination method

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