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two families go to a zoo. the smith family of two adults and three chidren pays £61 the jones family of three adults and five children pay £96. work out the price of an adult and child ticket, let a stand for adults and c stand for child

Respuesta :

irspow
2a+3c=61

2a=61-3c

a=30.5-1.5c

...

3a+5c=96, using a found above we get:

3(30.5-1.5c)+5c=96

91.5-4.5c+5c=96

91.5+0.5c=96

0.5c=4.5

c=9, and since a=30.5-1.5c

a=17

So adult tickets cost £17.00 and child tickets cost £9.00

The price of the ticket for an adult is £14.34 and the price of the ticket for a child is £9 and this can be determine by forming the linear equation in two variables.

Given :

  • The smith family of two adults and three chidren pays £61.
  • The jones family of three adults and five children pay £96.

Linear equation has to be form to determine the price of the ticket for an adult and a child.

Let 'a' be the price of ticket for an adult and 'c' be the price of ticket for a child than the linear equations will be:

2a + 3c = 61 --- (1)

3a + 5c = 96 --- (2)

Now, from equation (1) solve for 'a'.

[tex]\rm a = \dfrac{61-3c}{2}[/tex]   ---- (3)

Now, put the value of 'a' obtain in equation (3) in eqaution (2).

[tex]3\times\left(\dfrac{61-3c}{2}\right)+5c = 96[/tex]

[tex]183-9c+10c=192[/tex]

c = £ 9

Now, put the value of 'c' in equation(3).

[tex]a = \dfrac{61-(2\times9)}{3}[/tex]

a = £ 14.34

Therefore, the price of the ticket for an adult is £14.34 and the price of the ticket for a child is £9.

For more information, refer the link given below:

https://brainly.com/question/12420841

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