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 car hire company has x small cars and y large cars.
The company has at least 6 cars in total.
The number of large cars is less than or equal to the number of small cars.
The largest number of small cars is 8.
(a) Write down three inequalities, in terms of x and/or y, to show this information.
___ , ___ , ___ [3]
(b) A small car can carry 4 people and a large car can carry 6 people.
One day, the largest number of people to be carried is 60.
Show that \(2x+3y\leqslant 30\). [1]
(c)
By shading the unwanted regions on the grid, show and label the region R that satisfies all four inequalities. [6]
(d) (i) Find the number of small cars and the number of large cars needed to carry exactly 60 people.
___ small cars, ___ large cars [1]
(ii) When the company uses 7 cars, find the largest number of people that can be carried. [2]
Answer/Explanation
Ans:
9(a) x + y ⩾ 6 oe
y ⩽ x oe
x ⩽ 8
9(b) 4x + 6y ⩽ 60
9(c) Correct region indicated cao
9(d)(i) 6, 6
9(d)(ii) 34
Question
Klaus buys x silver balloons and y gold balloons for a party.
He buys
• more gold balloons than silver balloons
• at least 15 silver balloons
• less than 50 gold balloons
• a total of no more than 70 balloons.
(a) Write down four inequalities, in terms of x and/or y, to show this information.
………………………………………….
………………………………………….
………………………………………….
………………………………………….
(b) On the grid, show the information from part (a) by drawing four straight lines and shading the
unwanted regions.
(c) Silver balloons cost \($\)2 and gold balloons cost \($\)3.
Calculate the most that Klaus could spend.
\($ \)………………………………………..
Answer/Explanation
(a) y > x
x\geq 15
y< 50
x+y\leq 70
(b)Four correct ruled lines and correct region indicated
(c) 189