Thread: Help me please with an 11 + question for my daughter

Hi,

I am hoping someone out there will help me on this basic question below which has to be solved by my 10 year old daughter for her 11+. If it is possible please show simple working out.

Thanks

Dee

Question
On a bus route
The total cost of one ticket from G to J and one ticket from G to I is £1
The total cost of one ticket from G to J and one ticket from H to J is £1.20
The total cost of one ticket from G to J, one ticket from G to H, and one ticket
from I to J, is £1.30.
What is the cost of one ticket from G to J? _________

Let's assume that a ticket from G to J costs the same regardless if it is a direct ticket or an additional stop (H or I).

Then, if we buy all three combinations of tickets, we get:

• 3 tickets from G to J
• 1 ticket from G to H and 1 ticket from H to J
• 1 ticket from G to I and 1 ticket from I to J

So, what we actually get is:
5 tickets from G to J for the price of £1+£1.20+£1.30=£3.50

Hence one ticket from G to J costs £0.70.

Let's assume that a ticket from G to J costs the same regardless if it is a direct ticket or an additional stop (H or I).

Then, if we buy all three combinations of tickets, we get:

3 tickets from G to J
1 ticket from G to H and 1 ticket from H to J
1 ticket from G to I and 1 ticket from I to J

So, what we actually get is:
5 tickets from G to J for the price of £1+£1.20+£1.30=£3.50

Hence one ticket from G to J costs £0.70.

This implicitly uses the assumption that the cost is additive, that is that c(GJ)=c(GH)+c(HJ) etc.

Thank you very much for the swift response.

Brilliant

Dee