11 Plus Exams Forum

Hi,

Please help with below question b) and c) showing method:

Lemon, the mobile phone company, offers three different tariffs to its users:
TARIFF A
Pay £40 per month.
All calls free.
All texts free.

TARIFF B
Pay £20 per month.
10 calls free.
20 texts free.
After that, calls cost 15p each and texts cost 10p each.

TARIFF C
No monthly payment.
Each call costs 25p.
Each text costs 5p.


Tim uses tariff B.
(b) He sent 130 texts in January. He works out that he spent more using tariffB than he would have done using tariff A. What is the smallest number of calls he could have made?

(c) Stephen sent 100 texts in January. He works out that using tariff B would have cost him more than using tariff C. What is the largest number of calls that he could have made?

Tim uses tariff B.
(b) He sent 130 texts in January. He works out that he spent more using tariff B
(Pay £20 per month.
10 calls free.
20 texts free.
After that, calls cost 15p each and texts cost 10p each.)
than he would have done using tariff A
(Pay £40 per month.
All calls free.
All texts free.)
What is the smallest number of calls he could have made?

Fixed cost (£20) + texts (130-20)*10p = £11) + calls.
Calls must have cost more than £40-(£20+£11) i.e. more than £9
£9.00 / £0.15 = 60 paid for calls. But 10 were free so 70 total calls is the break even point.
Therefore he made at least 71 calls.

(c) Stephen sent 100 texts in January. He works out that using tariff B
(Pay £20 per month.
10 calls free.
20 texts free.
After that, calls cost 15p each and texts cost 10p each)
would have cost him more than using tariff C
(No monthly payment.
Each call costs 25p.
Each text costs 5p)
What is the largest number of calls that he could have made?

Cost of Fixed charge + texts + first 10 calls:
Tariff B - Fixed cost (£20) + texts (100-20)*10p = £8 + calls (10 free). -> £28 inc 10 calls free
Tariff C - Fixed cost (£0) + texts 100*5p = £5) + calls 10*25p each = -> £7.50

Difference £20.50. Difference in cost/call = 25p-15p = 10p.
So £20.50/£0.10 = 205
Therefore 205+10 = 215 calls is the breakeven point - the maximum of calls he could make before Tariff C becomes cheaper is 214

Thanks. Answers given are 71 and 214