Transcript Slide 1

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Mr & Mrs Phillips
Carpet Sales
A shop increased the price of its carpets by
20%, and sales of the carpets dropped by
20%
When Mr and Mrs Phillips married, the sum
of their ages was 44.
The difference between their ages was onesixth of the sum of their ages 10 years before
their marriage.
Did the shop’s profits from carpet sales rise
or fall?
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Eights and nines
The integers from 1 to 9 are listed on a
whiteboard
1, 2, 3, 4, 5, 6, 7, 8, 9
The mean of all the numbers in the list is 5.
Some extra eights and nines are added to the
list. The mean of the list is now 7.3
How many eights and nines are added?
How old were Mr and Mrs Phillips
when they married?
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At the table
There are six people in the Micklefield family: 2
parents, 2 girls and 2 boys. They all sit around the
table as shown.
The two girls never sit opposite
or next to each other.
The two boys never sit opposite or
next to each other.
The parents never sit opposite or next to each other.
How do the Micklefield family sit at the table?
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Mashed potatoes
Jay and Joy are peeling potatoes for a dinner
party, and they each start with the same number
of potatoes to peel.
Every minute, each of them peels two potatoes,
and Jay sneakily throws one of his unpeeled
potatoes on Joy’s pile.
After 10 minutes, Joy has three times as many
potatoes still to peel as Jay. How many potatoes
did each of them have to start with?
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Boxed in
The diagram shows a rectangular
box. The areas of the faces are 3,
12 and 25 square centimetres.
25cm2
12cm2
3cm2
What is the volume of the box?
If the areas of the faces are p, q
and r, what is the volume of the
box in terms of p, q and r?
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Cash point
Flash Jack went to the cash point. He drew out
the same amount of money as he had in his
pocket. He then spent £40 on CDs.
Jack went back to the cash point. He drew out
the same amount of money as he had in his
pocket. He then spent a further £40 on CDs.
Jack did this a third time.
He then had no money left. How much money
did he have with him to start?
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Overlap
5/
6
of the circle is shaded pink
4/
5
of the hexagon is shaded
yellow
Area of 15 circles = Area of ? hexagons
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10
A builder can build either luxury
houses or standard houses on a plot of
land.
Planning regulations prevent the
builder from building more than 30
houses altogether, and he wants to
build at least 5 luxury houses and at
least 10 standard houses.
Each luxury house requires 300m2 of
land, and each standard house
require 150m2 of land. The total
area of the plot is 6500m2.
Given that the profit on a luxury
house is £14000 and the profit on a
standard house is £9000, find how
many of each house he should build
to maximise his profit.
The object of this puzzle
to create a "fence" that
connects dots horizontally
or vertically, but not
diagonally. The numbers
in the grid indicate how
many sides of the fence
go around that space. Try
to find as many different
solutions as you can for
each problem. In the
example shown, there are
three different solutions.
Example
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Broom handles
A shop sells handles for garden
brooms which are made up of
cylinders of wood, diameter 5cm.
I bought three of these and, to
keep them together, put a rubber
band round each end of the
bundle. How long will each rubber
band be?
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Candlelight
One night two candles were lit, one of which
was 3cm longer than the other.
The longer one was lit at 5.30pm and the
shorter one at 7pm.
At 9.30pm they were both the same length.
The longer one burned out at 11.30pm and the
shorter one burned out at 11pm.
How long was each candle originally?
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Exactly how many minutes is it before six
o’clock if 50 minutes ago it was four times
as many minutes past three o’clock?
A 6 x 6 cube is painted red. It is
then cut up into a number of
identical cubes as shown in the
picture.
How many of the cubes have (a) 3 red faces
(b) 2 red faces (c) 1 red face (d) 0 red faces
What would the answers be for an n x n cube?
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Which is a better fit – a square peg in a
round hole or a round peg in a square hole?
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The diagram shows
a semi-circle and an
isosceles triangle
which have equal
areas. What is the
value of tan x°
x°
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Beverley’s watch gains 30 minutes every
hour, whilst Jason’s watch loses 30
minutes every hour. At midnight, they
both set their watches to the correct time
of 12 o’clock.
What is the correct time when their two
watches next agree?
The ratio a:b is 1:2, the ratio a:c
is 2:3, the ratio c:e is 1:4 and the
ratio d:e is 2:5
What is the ratio b:d in its
lowest terms?
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Rectangle problem
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A large rectangular piece of card is (√5 +
√20) cm long and √8 cm wide. A small
rectangle √2 cm long and √5 cm wide is cut
out of the piece of card.
What percentage of the
original rectangle
remains?
Word multiplication
In this multiplication each letter represents
a different digit between 0 and 9. Solve for
F, G, H, J and K.
(√5 + √20)
√8
F G H J K
X
4
K J H G F
√5
√2
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A large window consists of six square panes
of glass as shown.
Each pane is x m by x m
and all the dividing wood
is y m wide.
The total area of the glass is 1.5m2 and the
total area of the dividing wood is 1m2. Find
the values of x and y.
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The diagram shows two
circles and four equal
semi-circular arcs.
The area of the inner
shaded circle is 1.
What is the area of the
outer circle?
Answer sheet for …………………………………………
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14. 6 x 6: (a)
n x n: (a)
15.
16.
17.
18.
19.
20.
21.
22.
(b)
(b)
(c)
(c)
(d)
(d)
1. Fell by 4%
2. 20 years and 24 years
3. Fifteen 8s and six 9s, or six 8s and
fourteen 9s
B
P
4. E.g
P
11.
12.
13.
14.
G
G
B
5. 40
6. £35
7. w = 2.5cm, h = 1.2cm, l = 10cm,
volume = 30 cm2, volume = √pqr
8. 18
9. 13 luxury, 17 standard, profit
£335,000
10.
Answers
15.
16.
17.
18.
19.
20.
21.
22.
15 + 5π ≈ 30.7cm
24cm and 27cm
26 minutes
6 x 6: (a) 4 (b) 48
(c) 96
(d) 64
n x n: (a) 4 (b) 12(n-2) (c) 6(n-2)2 (d) (n-2)3
The circle covers more of the square than the square
does the circle. Therefore a round peg in a square
hole is a better fit.
π/2
12.00 midday – both watches will show 6.00
5:6
83.3%
F = 2, G = 1, H = 9, J = 7, K = 8
x = ½, y = ¼
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