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Homework 3: Business
Arithmetic 1, Indices and Logarithms
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Your score:
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Q1)
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The following are details of the charges from two
telephone companies:
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Company A charges a fixed amount of £ 25 per month
and gives 120 minutes worth of free calls.
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For anything over the 120 minutes, calls are
charged at 3 pence per minute.
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Company B has a fixed cost of £15, offers 60
minutes of free calls and charges 8 pence for each minute over 60.
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a)
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Find the monthly bill for
a user who makes 150 minutes worth of calls:
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with company A
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with company B
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b)
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How many minutes worth of
calls have been made with company A
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if the bill is £38.80?
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Company B offers a discount of 6% to those
customers who pay their bill online.
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c)
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Leia decides to pay her
bill online. What would be her new bill for
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making 150 minutes worth of calls? Answer to 2
decimal places.
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d)
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If m
minutes worth of calls are made per month, write an expression for the
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total cost c in pounds for each company (ignoring any online discounts).
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A:
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c =
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for m < 120
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c =
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m +
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for m ≥ 120
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B:
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c =
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for m < 60
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c =
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m +
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for m ≥ 60
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e)
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Find the number of
minutes used for which the bill from both companies would be equal:
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(Ignore any online discounts.)
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number of minutes:
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rounded to nearest
minute.
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cost of bill:
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Q2)
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Andrea's company makes chocolate animals sold in
boxes of 12. Each animal is made from 16g of chocolate.
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The empty boxes cost £ 0.20 each and 1 kg of chocolate costs £ 25.
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a) How many chocolate animals can be made from 1 kilogram of
chocolate?
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b) How many boxes can she fill with chocolate animals?
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c) What are her total costs making this many boxes given she
bought 1 kg of chocolate?
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d)
She sells boxes for £ 6.50 each, what is her percentage profit margin?
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e)
How much should she sell each box for to have a profit margin of 25% ?
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Q3)
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A car
rental company and decides to offer two types of tarrif:
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Tarrif A: No fixed fee but a charge of £ 1.40 per
mile travelled.
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Tarrif B: A fixed fee of £250 plus £0.12 per mile
travelled.
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For both tarrifs, the customer must also pay £0.65
per mile for petrol.
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a)
If a customer travels 380
miles, calculate the cost under each tarrif:
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Cost under tarrif A:
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Cost under tarrif B:
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b)
Let x be the number of
miles travelled and let y
be the total cost.
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Write down an expression for y in terms of x for each tarrif:
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A
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y =
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x +
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B
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y =
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x +
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c) The total cost is the same for both tariffs, find:
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i)
the number of miles travelled:
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ii)
the total cost:
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Q4)
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a)
VAT at 19.5% is added
to the price of all goods. If a digital radio is £
105.10
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before the VAT is added, what is its price after the VAT is added?
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b)
Celia bought an oven for £650. The price included the VAT.
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What was the price of the oven before the VAT was
added?
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Q5)
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The value of an investment fund is given by the
equation V = 8400 (1.032)n
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where n is the number of years after the initial investment.
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a) What is the value of the initial investment?
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b) How long until the investment is worth £12,000?
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years
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c) How long until the investment triples in value?
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years
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Q6)
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Express (1/2) log464 x14 – 2 log44 x2 + 3 in the form log4( a x b)
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log
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x
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4
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