The entry ticket for an exhibition is rs. 5 for children and rs. 15 for adults. A group of 13 persons visited this exhibition and paid rs. 115 tobuy entry ticket find the number of children and adults
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Given :
- An entry ticket for an exhibition, costs ₹5 for children and ₹15 for adults
- A group of 13 persons visit the exhibition and pay ₹115 in total.
Aim :
- To find the number of children and adults respectively,
Solution :
Let the total number of children be x and number of adults be y.
- Total number of persons = 13
→ x + y = 13
Transposing y to the other side,
→ x = 13 - y
- According to the question, the cost of ticket for one child is ₹5.
Therefore, for x number of children, the cost = ₹5 × x → ₹5x
- The cost of a ticket for one adult is ₹15.
Hence, for y number of adults, the cost = ₹15 × y → ₹15y
Forming a Linear Equation,
⇒ 5x + 15y = 115
Substituting x for 13 - y,
⇒ 5(13 - y) + 15y = 115
⇒ 65 - 5y + 15y = 115
⇒ 65 + 10y = 115
Transposing 65 to the other side,
⇒ 10y = 115 - 65
⇒ 10y = 50
Transposing 10,
Reducing to the lowest terms,
⇒ y = 5
∴ The number of adults are 5 and number of children are 8 (13 - 5 → 8)
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