200 tickets were sold for a show. VIP tickets costs ₦1,200 and ₦700 for regular. Total amount realised from…

Analysis

To solve this problem, we need to set up a system of linear equations based on the information provided:

1. The total number of tickets sold.
2. The total amount of money realized from those sales.

Concept

We will use the Substitution or Elimination method for simultaneous equations. Let:

• $x$ = number of VIP tickets
• $y$ = number of regular tickets

Step-by-Step Solution

Step 1: Form the equations.

• From the total number of tickets: $x + y = 200$ --- (Equation 1)
• From the total amount realized: $1200x + 700y = 180,000$ --- (Equation 2)

Step 2: Simplify Equation 2. To make the calculation easier, divide Equation 2 by 100: $12x + 7y = 1800$ --- (Equation 3)

Step 3: Solve using substitution. From Equation 1, express $y$ in terms of $x$: $y = 200 - x$

Substitute this into Equation 3: $12x + 7(200 - x) = 1800$ $12x + 1400 - 7x = 1800$

Step 4: Solve for $x$. $12x - 7x = 1800 - 1400$ $5x = 400$ $x = \frac{400}{5}$ $x = 80$

Step 5: Solve for $y$. Substitute $x = 80$ back into Equation 1: $80 + y = 200$ $y = 200 - 80$ $y = 120$

So, 80 VIP tickets and 120 regular tickets were sold.

Conclusion

Comparing our result ($x=80, y=120$) with the given options, it matches option D.

Exam Tip

When you have a system of equations in a multiple-choice exam, you can save time by testing the options. For example, in option D: $80 + 120 = 200$ (Correct total tickets). Then check the money: $(80 \times 1200) + (120 \times 700) = 96,000 + 84,000 = 180,000$. Since this matches the total amount, you don't even need to do the full algebra!