O lvl E Maths: Applications in Practical Situations

Question from http://www.sgforums.com/forums/2297/topics/334900

The normal price of a roll of film for 36 photographs is $8.99.
The normal price of printing 36 photographs is $17.65 for each roll of film.

(a) Show that the cost of each photograph is 74 cents.


(b) Shop A offers '4 rolls of film for the price of 3'.
The price of printing 36 photographs remains at $17.65 for each roll of film.
Kim bought 4 rolls of film at Shop A and had the photographs printed there.

Calculate how much each photograph cost her, to the nearest cent.


(c) Shop B kept the price of each roll of film at $8.99. If offered a 20% off the normal price for printing the photographs.
Sue bought one roll of film at shop B and had the photographs printed there.

Calculate how much each photograph cost her, to the nearest cent.


(d) Ali decided to buy 4 rolls of film at Shop A and have his photographs printed at Shop B.

Calculate the percentage reduction in cost of each of his photographs compared to the cost in (a).

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Answer:

(a) Cost of each photograph = ($8.99 + $17.65) / 36 = $0.74 (shown)

(b) Cost of each photograph = ($8.99 * 3 + $17.65 * 4) / (36 * 4)
= $95.57 / 144
= $0.677
= $0.68 (to nearest cent)

(c) Cost of each photograph = ($8.99 + $17.65 * 0.8) / 36
= $23.11 / 36
= $0.641
= $0.64 (to nearest cent)

(d) Cost of each photograph = ($8.99 * 3 + $17.65 * 4 * 0.8) / (36 * 4)
= $83.45 / 144
= $0.579
= $0.58 (to nearest cent)

Percentage reduction = (0.74 - 0.58) / 0.74 * 100%
= 0.16 / 0.74 * 100%
= 21.62%
= 21.6% (3 s.f.)

O lvl E Maths: Applications in Practical Situations

Andrew is buying a television set priced at $1850 and has three payment options:

Option 1: Pay cash and receive a discount of 8.5%
Option 2: Pay a deposit of $500 followed by 12 monthly payments of $122
Option 3: Purchase it on finance at a compound interest of 9.25% per annum payable over 2 years

(a) Calculate the amount, in the nearest cent, Andrew will pay for each of the three options.

(b) If Andrew pays a deposit of $500 and borrows the remainder at 9.25% per annum for 1 year, will he pay less than if he chooses option 2? Explain.

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Answer:

(a)
Option 1: Andrew will pay $1850 - $1850*8.5% = $1692.75

Option 2: Andrew will pay $500 + 12 * $122 = $1964

Option 3: Andrew will pay $1850 * 109.25% * 109.25% = $2208.08


(b) $1850 - $500 = $1350
Total paid if Andrew pays a deposit of $500 and borrows the remainder at 9.25% per annum for 1 year
= $500 + $1350 * 109.25% = $1974.88

Andrew would pay $10.88 less if he chooses Option 2.

O lvl E Maths: Applications in Practical Situations

John invest $4750 in a bank that pays a compound interest at the rate of n% per year, Find the value of n if John has $6250 after 7 years.

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Answer:

P(1+r/100)ⁿ

Principle = $4750
Rate = n
Years = 7

Thus,

4750 (1 + n/100)⁷ = 6250
(1 + n/100)⁷ = 6250/4750
1 + n/100 = 7√(6250/4750)
n/100 = 1.039988 - 1
n = 0.039988 x 100
n ≈ 4