It is currently Fri Dec 09, 2016 3:53 am

 All times are UTC

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: MGS 2007 Q13 MathPosted: Tue Oct 22, 2013 1:42 pm

Joined: Wed Dec 14, 2011 9:54 am
Posts: 211
Hi,

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?

Top

 Post subject: Re: MGS 2007 Q13 MathPosted: Tue Oct 22, 2013 2:07 pm

Joined: Mon Aug 22, 2011 8:20 pm
Posts: 1706
Location: Warwickshire
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

Top

 Post subject: Re: MGS 2007 Q13 MathPosted: Tue Oct 22, 2013 2:34 pm

Joined: Wed Dec 14, 2011 9:54 am
Posts: 211
Thanks. Answers given are 71 and 214

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC

#### Who is online

Users browsing this forum: No registered users and 1 guest

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ FORUM RULES    Forum Rules and FAQs 11 PLUS SUBJECTS    VERBAL REASONING    MATHS    ENGLISH    NON-VERBAL REASONING    CEM 11 Plus GENERAL    GENERAL 11 PLUS TOPICS    11 PLUS APPEALS    11 PLUS TUTORS    INDEPENDENT SCHOOLS    11 PLUS CDs/SOFTWARE    11 PLUS TIPS    PRIMARY    SEN and the 11 PLUS    EVERYTHING ELSE .... 11 PLUS REGIONS    Berkshire    Bexley and Bromley    Birmingham, Walsall, Wolverhampton and Wrekin    Buckinghamshire    Devon    Dorset    Essex    Essex - Redbridge    Gloucestershire    Hertfordshire (South West)    Hertfordshire (Other and North London)    Kent    Lancashire & Cumbria    Lincolnshire    Medway    Northern Ireland    Surrey (Sutton, Kingston and Wandsworth)    Trafford    Warwickshire    Wiltshire    Wirral    Yorkshire BEYOND 11 PLUS    Beyond 11 Plus - General    GCSEs    6th Form    University