Question

An amusement park sells two kinds of tickets. Tickets for children cost 1.50 Rs. Adult tickets cost 4 Rs. On a certain day 278 people entered the park. On that day the admission fees collected totalled 792 Rs. How many children and adults were admitted that day ?

Answer 1

Answer:

128, 150

Step-by-step explanation:

Let the number of children admitted be 'x' and the adults be 'y'.

(i) On a certain day the admission fees collected 792.

x + y = 278

(ii) Tickets for children 1.50 adult tickets, adult tickets cost 4.

1.5x + 4y = 792

On solving (i) * 4 & (ii), we get

4x + 4y = 1112

1.5x + 4y = 792

----------------------

2.5x = 320

x = 128.

Substitute x = 128 in (ii), we get

⇒ 1.5x + 4y = 792

⇒ 1.5(128) + 4y = 792

⇒ 192 + 4y = 792

⇒ 4y = 792 - 192

⇒ 4y = 600

⇒ y = 150.

Therefore:

The number of children admitted that day = 128.

The number of adults admitted that day = 150.

Hope it helps!

Answer 2

Suppose the number of children admitted be 'M'  

The adults = 'Q'.

1.) 792 admission fees collected on a certain day.

→ 278 people entered the park

m + q = 278 [Eqn (1)]

2.) Tickets for children is 1.50 and for adult tickets cost is 4.

1.5m + 4q = 792 [Eqn (2)]

Multiply (1) by 4 and (2) we get :-

m = 128.

Put the value of m = 128 in (2), we get

⇒ 1.5(128) + 4q = 792

⇒ 192 + 4q = 792

⇒ 4q = 792 - 192

⇒ 4q = 600

⇒ q = $\bfhuge\frac{600}{4}$

⇒ q = 150.

Hence

Number of children admitted that day = 128.

Number of Adult admitted that day = 150.