Name : ____________________ Date : _____________
Score : _____________
Write down your correct answer and show your workings:
1) Apple and Berth
had a total of $300 to spend.
Apple spent thrice of the amount she has left while Berth spent twice of
the amount she has left.
Given that the 2 total friends had a total of $90 left, how much did they
have at first?
Ans: ____________________
2) The number of apples at
a store was 80% more than the number of oranges.
After 60% of the oranges were sold, there were 42 more apples than oranges.
Find the total number of apples and oranges at first.
Ans: ____________________
3) The figure below, which
is not drawn to scale, is made up of a rhombus ABCF and a parallelogram
CDEF.
Given
that < YCB = 47 degree, find < EDC.
Ans: ____________________
4) Danny had $156 more than
Esther.
After
Danny had spent 1/6 of his money and Esther spent 1/2 of her money,
Danny
had $245 more than Esther.
How much
money did Danny have at first?
Ans: ____________________
5) A florist sold twice
as many roses as tulips and collected $400 in total.
She collected $80 more on the tulips than the roses.
Given that a tulip costs $2 more than a rose, find the cost of a rose.
Ans: ____________________
Answers:
1) Let A be 1 unit of Apple's amount.
Let B be 1 unit of Berth's
amount.
At the beginning : 4A +
3B = $300 ......(1)
At the end : A + B = S$90
=> 3A + 3B = $90
x 3 = $270..... (2)
Comparing (1) and (2) => A = $30
Since Apple has 4 units at first, she will have $30 x 4 = $120
Total at first is $300.
Therefore, Berth's share at first is $180.
or
2) Apples : Oranges = 180 : 100
= 9u : 5u,
Total = 14u
After 60% Oranges sold,
Oranges left = 0.4 x 5u
= 2u
So 9u-2u = 42,
7u=42,
1u =6
Total number of fruits
at first: 14u = 84,
54 apples and 30 oranges.
3) Based on the figure,
YC = YA, i.e. Angle YCA
= (180 - 118)/2 = 31 (base angles of isos triangle)
Angle ACB = Angle YCA
+ Angle YCB = 31 + 47 = 78
Since ABCF is a rhombus,
then AB = BC, Angle CAB = Angle ACB
Angle ABC = 180 - 78x2
= 24 (sum angles in a triangle)
Angle EDC = 180 -24 =
156 ( interior angles, AB // FC // ED)
4)
2u = 245 - 130
= 115
Danny had 6u + 156 at first
= 3 x 115 +156
= 501
5) First, find the total cost for roses and tulips
respectively :
Total cost of roses =
(400-80)/2 = $160
Total cost of tulips =
$400 - $ 160 = $240
The florist sold twice
as many roses as tulips.
Assume we put same number
of flowers in each packet, we would have 1 packet of tulips and 2 packets
of roses.
Now, each packet of tulips =
$ 240
Each packet of roses = $ 160
/ 2 = $80
Since each tulip cost $2 more than a rose, number of flowers in each packet = (240-80)/2 = 80
So, number of tulips = 80, number of roses = 80 x 2 = 160