Question

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

Answer 1

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,

$\implies \sf y = \dfrac{50}{10}$

Reducing to the lowest terms,

⇒ y = 5

∴ The number of adults are 5 and number of children are 8 (13 - 5 → 8)