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Answer : Sarah bought 4 first class tickets and 3 coach tickets.
Explanation :
We will call F the number of first class tickets and C the number of coach tickets.
Sarah had to buy a total of 7 tickets for 7 people.
Then F + C = 7 (Equation 1)
She used her total budget = $5,620
Then F*$1,150 + C*$340 = $5,620 (Equation 2)
F + C = 7
F = 7 - C
Now we can replace the value F in the equation 2
(7 - C)*$1,150 + C*$340 = $5,620
7*$1,150 - C*$1,150 + C*$340 = $5,620
$8,050 - C*$810 = $5,620
$8,050 - $5,620 = C*$810
$2,430 = C*$810
C = $2,430/$810 = 3 => number of coach tickets
F = 7 - C = 7 - 3 = 4 => number of first class tickets
Answer : Sarah bought 4 first class tickets and 3 coach tickets.
Verification
Replacing these values in equation 2
4*$1,150 + 3*$340 = $4,600 + $1,020 = $5620 => total budget