200 tickets were sold for a show. VIP tickets costs ₦1,200 and ₦700 for regular. Total amount realised from the sale of the tickets was ₦180,000. Find the number of VIP tickets sold and the the number of regular ticket sold.
Let \(x\) = number of VIP tickets sold and
\(y\) = number of regular tickets sold
Total number of tickets sold = 200
⇒ \(x\) + \(y\) = 200 ---- (i)
If it costs ₦1,200 for a VIP ticket, then it costs ₦1200x for \(x\) number of VIP tickets sold and
If it costs ₦700 for a regular ticket, then it costs ₦700\(y\) for \(y\) number of VIP tickets sold
The total amount realised from the sale of tickets = ₦180,000
⇒ 1200\(x\) + 700\(y\) = 180000 ----- (ii)
From equation (i)
\(x\) = 200 - \(y\) ----- (iii)
Substitute (200 - \(y\)) for \(x\) in equation (ii)
⇒ 1200(200 - \(y\)) + 700\(y\) = 180000
⇒ 240000 - 1200\(y\) + 700\(y\) = 180000
⇒ 240000 - 500\(y\) = 180000
Collect like terms
⇒ 240000 - 180000 = 500\(y\)
⇒ 60000 = 500\(y\)
⇒ \(y = \frac{60000}{500} = 120\)
Substitute 120 for \(y\) in equation (iii)
⇒ \(x = 200 - 120\)
⇒ \(x = 80\)
∴ The total number of VIP tickets sold is 80 and regular is 120
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