Test Paper Problem Question. Can You Help?

[11Eleven2017]

Hi.. have seem this type of question on several test papers. Not sure how to explain to DC how to approach it. Can you help?
Find the price of the adult/child ticket.
1 adult, 4 children go to fairground. Total cost £64. Child ticket is 25% less than adult ticket. What are their respective ticket prices.

25 % is a quarter 1/4 so 4 children are the same as one adult.
The cost for 1 adult and 4 children is therefore the same as 2 adults.
£64 divided by 2 is £32 so the adult ticket costs £32.
£32 divided by 4 is £8 so the cost of a child ticket is £8.

Child ticket is 25% less

not 25% of the adult's ticket

Child ticket is 75%
Adult ticket is 100%

(4 x 75) + 100 = 400

64÷400 x 75 = 12 (child)

4 x 12 = 48

64 - 48 = 16 (adult)

Each child costs 75% or 3/4 of the price of an adult. So 4x75% =300% which is the same as 3 adults.
So 1 adult and 4 kids is the same price as 4 adults.
Divide the 64 by 4=16, so one adult is £16.
Then reduce the £16 by 25% giving £12 for a child.

Each child is paying 75% of the adult price, ie 3/4. 4 lots of 3/4 = 3. So the four children are paying the same as 3 adults. Add in the actual adult and the £64 is the cost of 4 adult tickets. 1 adult must cost £16 and each child £12.

Dang those slow fingers!

I did it this way

Child ticket is 3/4 of adult ticket.

So, if adult ticket is 4X, child ticket is 3X

4X + 3X + 3X + 3X + 3X = 64

16X = 64

X = 4

Therefore adult ticket, 4X = 16

Child ticket, 3X = 12

The cost for a child ticket is 75% of an adult ticket.
Four children's tickets therefore add up to 300% of an Adults ticket, therefore the equivalent of 3 adults.

Add that to the existing adult and divide into 64 (64/4) =16

So £16 per adult and £12 per child (3/4 of £16)

25% ie equivalent to 1/4
After a discount, the four children each pay 3/4 of an adult ticket.
3/4 + 3/4 + 3/4 +3/4 is 3.

So, an equivalent of 4 adult tickets were bought.
64 / 4 = 16
3/4 of 16 = 12

Again using algebra, you could also do it this way (which is exactly what all the other posters have said, just shoving the letters for unknowns in)

3/4 A = C (where A is an adult ticket and C is a child)

A + 4C = 64

A + 4(3/4A) = 64

A + 3A = 64

4A = 64

A = 64/4 = 16

So, if C = 3/4A

C = 3/4 x 16

C = 12

£64 /5 tickets = £12.80
how is this relevant?

ah see you've deleted.

Aren't most papers multiple choice these days? If it were the case you could eliminate the obviously wrong ones and then try adding up the others to see which one works.

I approached it:

Child ticket (c) is 3/4 of adult ticket (a)

1a + 4c = £64
1a + 4c = 1a + 4×(3/4a) = 1a + 3a = 4a
》4a = £64; a = £16

c = 3/4a = £48/4 = £12

Adult tickets are £16; Child tickets are £12.

Absolutely love mumsnet... ask a question and get so many lovely helpful responses... GREAT! Thanks guys x

that is bloody hard for a 10/11 year old though!
(or for a 42 year old with GCSE A maths!)

if it was 1 adult and 4 child tickets, a child ticket is 25% of the cost of an adult ticket. Total cost £64 - what are the costs of each ticket? Even that would be tricky though doable. these kids are going into secondary almost ready for GCSE maths .