Question
Raheem makes baskets and mats.
Each week he makes x baskets and y mats.
He makes fewer than 10 mats.
The number of mats he makes is greater than or equal to the number of baskets he makes.
(a) One of the inequalities that shows this information is y< 10.
Write down the other inequality.
………………………………………….
(b) He takes \(2\frac{1}{4}\) hours to make a basket and \(1\frac{1}{2}\) hours to make a mat.
Each week he works for a maximum of 22.5 hours.
Show that \(3x+2y\leq 30.\)
(c) On the grid, draw three straight lines and shade the unwanted regions to show these inequalities.
(d) He makes \($40\) profit on each basket he sells and \($28\) profit on each mat he sells.
Calculate the maximum profit he can make each week.
\($ …………………………………………\)
Answer/Explanation
(a) y ⩾ x
(b) 2.25x + 1.5y ⩽ 22.5
One step shown to
3x + 2y ⩽ 30
(c) y = 10 ruled
3x + 2y = 30 ruled
y = x ruled
Correct region indicated
(d) 412
Question
(a) The price of a book increases from \($\)2.50 to \($\)2.65 .
Calculate the percentage increase.
% [3]
(b) Scott invests \($\)500 for 7 years at a rate of 1.5% per year simple interest.
Calculate the value of his investment at the end of the 7 years.
\($\) [3]
(c) In a city the population is increasing exponentially at a rate of 1.6% per year.
Find the overall percentage increase at the end of 20 years.
% [2]
(d) The population of a village is 6400.
The population is decreasing exponentially at a rate of r% per year.
After 22 years, the population will be 2607.
Find the value of r.
r = [3]
Answer/Explanation
Ans:
8(a) 6 nfww
8(b) 552.5[0]
8(c) 37.4 or 37.36…
8(d) 4[.00…]
Question
(a) The price of a house decreased from \($82500\) to \($77500.\)
Calculate the percentage decrease.
……………………………………. %
.(b) Roland invests\( $12000\) in an account that pays compound interest at a rate of 2.2% per year.
Calculate the value of his investment at the end of 6 years.
Give your answer correct to the nearest dollar.
\($ ………………………………………..\)
Answer/Explanation
(a) 6.06 or 6.060 to 6.061
(b) 13 674