Unit 9
9 marks · NormalA shop in the UK is selling a calculator for £28.50. In another country, the same calculator costs $36.
The exchange rate is £1 = $1.20.
Convert the UK price of the calculator into dollars. Give your answer to 2 decimal places.
Hence, prove that buying the calculator in the UK is a better deal, and explain your reasoning.
Let be the price in pounds, and be the price in dollars, with the exchange rate .
Write a general proof that shows for any UK price and other country price , the UK is the better deal if .
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) $34.20 USD
(b) The converted UK price ($34.20) is less than the other country’s price ($36), so buying in the UK is a better deal.
(c) If UK price is , then in dollars it is . If , then the UK price converted is less than the other country price, so the UK is the better buy.
Common mistakes: Multiplying instead of dividing when converting currencies; Incorrect logic in explanation; Not using algebraic proof
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Multiplies £28.50 by 1.20 or correctly sets up the calculation.
A1 (a) · 1 mark · Calculates $34.20 (accept 2 dp).
M2 (b) · 1 mark · Compares converted UK price to $36. (follow-through)
A2 (b) · 1 mark · Correct argument that $34.20 < $36, so UK is better. (follow-through)
B1 (b) · 1 mark · States clear, explained reasoning (UK is better as its price is lower after conversion).
M3 (c) · 1 mark · Uses algebra, sets up and .
A3 (c) · 2 marks · Shows and explains that means the UK price is better; stepwise valid logical deduction.
B2 (c) · 1 mark · Writes a complete proof in words or algebraical phrase.
Worked solution
a) To convert £28.50 to dollars: .
The price in dollars is $34.20.
b) The US price is $36. $34.20 < $36 so buying in the UK costs less after conversion. Therefore, buying the calculator in the UK is the better deal.
c) Let the UK price be pounds, so in dollars this is . The other country’s price is dollars.
If , then after converting, the UK price is less. Therefore, whenever , the UK is the better deal.