Question
(a) A shop sells dress fabric for \($\)2.97 per metre.
(i) A customer buys 9 metres of this fabric.
Calculate the change he receives from \($\)50.
\($\) ………………………………………..
(ii) The selling price of \($\)2.97 per metre is an increase of 8% on the cost price.
Calculate the cost price.
\($\) …………………………. per metre
(b) A dressmaker charges \($35\) or 2300 rupees to make a dress.
Calculate the difference in price when the exchange rate is 1 rupee=\($\)0.0153 .
Give your answer in rupees.
………………………………. rupees
(c) The dressmaker measures a length of fabric as 600m, correct to the nearest 5 metres.
He cuts this into dress lengths of 9m, correct to the nearest metre.
Calculate the largest number of complete dress lengths he could cut.
…………………………………………
Answer/Explanation
(a)(i) 23.27 final answer
(ii) 2.75 final answer
(b) 12.4[0] or 12.41 to 12.42
(c) 70 nfww
Question
Marianne sells photos.
(a) The selling price of each photo is \($6.\)
(i) The selling price for each photo is made up of two parts, printing cost and profit.
For each photo, the ratio printing cost : profit = 5 : 3.
Calculate the profit she makes on each photo.
\($ ……………………………………….. \)
(ii) Calculate her profit as a percentage of the selling price.
……………………………………..%
(iii) Calculate the selling price of a photo in euros (€) when the exchange rate is €1 =\( $1.091\)
€ ………………………………………..
(b) Marianne sells two sizes of photo.
These photos are mathematically similar rectangles.
The smaller photo has length 15cm and width 12cm.
The larger photo has area \(352.8cm^2.\)
Calculate the length of the larger photo.
…………………………………… cm
(c) In a sale, Marianne buys a new camera for \($483.\)
This is a reduction of 8% on the original price.
Calculate the original price of the camera.
\($ ……………………………………….. \)
Answer/Explanation
(a)(i) 2.25 final answer
(ii) 37.5
(iii) 5.5[0] or 5.499 to 5.500
(b) 21
(c) 525
Question
Apples cost x cents each and oranges cost (x + 2) cents each.
Dylan spends $3.23 on apples and $3.23 on oranges.
The total of the number of apples and the number of oranges Dylan buys is 36.
(a) Write an equation in x and show that it simplifies to \(18x^2 – 287x – 323 = 0\).
(b) (i) Find the two prime factors of 323.
(ii) Complete the statement.
\(18x^2 – 287x – 323 = (18x …………….)(x…………………….)\)
(iii) Solve the equation \(18x^2 – 287x – 323 = 0\)
x = ………………. or x = ……………………
(c) Find the largest number of apples Dylan can buy for $2.
Answer/Explanation
Answer:
(a) \(\frac{323}{x} + \frac{323}{x + 2} = 36\) oe three term equation
323(x + 2) + 323x = 36x(x + 2) oe
or \(\frac{323x + 343 + 323x}{x(x+2)}=36\) oe
\(36x^2 – 574x – 646 = 0\)
\(18x^2 – 287x – 232 = 0\)
(b) (i) 17, 19
(ii) ( ……. + 19)(………. – 17)
(iii) 17, – \(\frac{19}{18}\) oe
(c) 11 cao