In a sports meet, tickets for adults cost ₹150 each and tickets for children cost ₹100 each. A total of 200 people attended the meet, and the total amount collected from ticket sales was ₹25,000. (Let the number of adult tickets sold be x and the number of children’s tickets sold be y.) Frame a pair of linear equations in x and y to represent this situation.
Answer: x + y = 200 (people) and 150x + 100y = 25000 (money), i.e. 3x + 2y = 500.
Step-by-step solution
Idea: There are two totals: one counts people and one counts money. Each total gives one equation.
- Number of people: adults + children = 200, so x + y = 200.1 mark
- Money: 150 × x + 100 × y = 25000, so 150x + 100y = 25000, which simplifies (÷ 50) to 3x + 2y = 500.1 mark
x + y = 200 and 150x + 100y = 25000 (or 3x + 2y = 500).
Check: Solving: 3x + 2y = 500 and 2x + 2y = 400 give x = 100, y = 100: 15000 + 10000 = 25000 ✓.
Answer to write in the exam
Total people: x + y = 200
Total collection: 150x + 100y = 25000, i.e. 3x + 2y = 500
∴ The pair: x + y = 200, 3x + 2y = 500
Common mistakes that cost marks
- Writing x + y = 25000, mixing the number of people with the money.
- Writing 150 + 100 = 25000 with no variables.
How this can come in the exam
MCQ (1 mark)
A shop sold 40 shirts, some at ₹300 and the rest at ₹500, for ₹15,600. If a shirts were sold at ₹300 and b at ₹500, the equations are
- a + b = 15600, 300a + 500b = 40
- a + b = 40, 300a + 500b = 15600
- a + b = 40, 500a + 300b = 15600
- a − b = 40, 300a + 500b = 15600
Show answer
(B) a + b = 40, 300a + 500b = 15600
Count: a + b = 40; money: 300a + 500b = 15600.
Try one yourself
A purse has 30 coins of ₹5 and ₹10 worth ₹220 in all. Form the equations.
Show answer
With x five-rupee and y ten-rupee coins: x + y = 30, 5x + 10y = 220.
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