Name : ____________________ Date : _____________
Score : _____________
Write down your correct answer and show your workings:
1) Ali, Billy and Caven
had some cards.
Ali would have twice as many cards as Billy if Billy gave 28 cards to Ali.
Both Billy and Caven would have the same number of cards if Caven gave
84 cards to BIlly.
Given that Caven had 112 more cards than Ali at the beginning, find the
number of cards each of them had at the beginning.
2) Elynn, Fiona and
Greg had a total of 336 cards.
First Elynn gave Fiona as many cards as Fiona had.
Then Fiona gave Greg as many cards as Greg had, and finally Greg gave Elynn
as many cards as Elynn had left.
In the end, all of them had the same number of cards.
How many cards did Elynn have at first?
3) There were 180 tomatoes
and carrots in a basket at first.
2/5 of the tomatoes and 2/3 of the catrrots were used for cooking.
In the end, there were 80 tomatoes and carrots left in the basket.
How many:
a) tomatoes were there at first?
b) carrots were used in the cooking?
4)
5) A tiger and a leopard
are 60km apart.
The tiger runs at a speed of 55km/h.
At the same time, the leopard runs towards the tiger at a speed of 25km/h.
How much further will the tiger have run than the leopard when the two
animals meet?
Answers:
1)
Notes:
The first scenario is Billy giving to Ali.
Ali has 196 cards and Billy has 140 cards. If Billy gives
28 cards to Ali, he will have 112 cards and Ali, 224 cards. Therefore,
Ali has twice as much as Billy.
The second scenario is Caven giving 84 cards to Billy. Caven has 308 cards at first (196+112).Billy has 140 cards. After receiving 84 cards from Caven, he’ll have 224 cards. After giving away 84 cards, Caven will have 224 cards, which is equal to that of Billy.
If you are wondering why Billy’s 224 cards(after receiving 84 cards from Caven) is equal to that of Ali (after receiving 28 from Billy). This refers to the after events of two different scenarios.This is also the important first step to the solution,where you get your one unit equals to 112 ( 84+28 )
2)
E F G
at the end (336 divide 112 112 112 by 3)
back a step divide by 2 +56
=56 =168
back a step +84 divide by 2
=196 =84
back a step +98 divide by 2
=154 =98
Therefore had E had 154 cards at first.
Notes:
back 1st step, the divide by 2=56 is for E. 112+56=168
for G
back 2nd step, 112+84=196 is for F, G is 168 divide by 2=84
back a step, E is 56+98=154, F is 196 divide by2=98
3)
4)
Let area of ABF = 1 unit cm2
So, area of FED = (1 unit +7) cm2
Area of BCE = (1/2 X 14 X 10) cm2 = 70 cm2 = Area BCDF + (1 unit +7) cm2
1 unit + Area BCDF = 63 cm2
14 x AB = 63
AB = 4.5 cm
5)
For every 1 hour, the two animals ran -> 55 + 25 = 80
km
If total distance is 60 km, that will take 60 / 80 = ¾ hour
So the two animals will take ¾ hour (45 mins) to meet.
(55-25) km/hr X ¾ hr -> 30 x ¾ = 22.5 km
or
For fixed time taken, the ratios of speed and distance of tiger to leopard are ..
Tiger Leopard
Speed 11 : 5
Distance 11 : 5
16units =60km
2units = 7.5km
6units = 22.5km
The tiger would have run 22.5 km further than the leopard when they meet.