Mr Tan originally had some oranges for sale. After three customers bought portions of the remaining oranges and received free oranges, Mr Tan had 1 dozen (12) oranges left. Working backwards, the initial number of oranges Mr Tan had was calculated to be 216.

1. Mr Tan had some oranges for sale. The first customer bought 1/2 of the oranges
and received 8 oranges free. The second customer bought 45% of the remaining and
received 5 free oranges free. The third customer bought 70% of the remaining
oranges and received 3 oranges free. Mr Tan then had 1 dozen oranges left. How
many oranges did he have at first?
This is what I gathered from the question but I can't solve it, pls help:
1st Customer bought =1/2u+ 8 oranges
Remaining =1/2u- 8 oranges
2nd Customer bought = 45% of (1/2u-8 oranges)
Remaining = 55% of (1/2u-8oranges)
3rd Customer bought = 70% of 55% of (1/2u-8oranges)
Remaining = 30% of 55% of (1/2u-8 oranges)= 12 oranges
1u=16
Pls help as I am unable to get d answer. Tks
Work backwards to get to the initial number.
Steps:
Quantity Left ---- Quantity Bought
Initial ---- 1st: ½ Initial + 8
½ initial–8=R1 ---- 2nd : 45% of R1 + 5
55% of R1-5=R2 ---- 3rd: 70% of R2 + 3
30% of R2- 3 = 12
work backwards,
30% of R2 = 15, R2 = 15/3 x 10 = 50
55% of R1 – 5 = R2 = 50, R1 = 55/55 x 100 = 100
½ initial -8 = R1 = 100, Initial = 108 x 2 = 216
Before a game, Azmi and Peiqin had the same no. of pitcure cards. During the
first round, Azmi lost 12 of his picture cards to Peiqin. During the second
round, Peiqin won 16 picture cards from Azmi. In the end, Peiqin had 3 times as
many picture cards as Azmi.
a) How many more picture cards did Peiqin have in the end?
b) How many pitcure cards did both of them have in all?
a)
Azmi= 1u
Peiqin=3u+28
2u=28
1u=14
3u+28=3x14+28=56 picture cards
b) 4u+28=84 picture cards
Part a) is correct but for part b) the answer sheet shows 112? Appreciate help
on part b) pls. Tks
answer:
http://www.kiasuparents.com/kiasu/forum/viewtopic.php?
f=27&t=6373&p=517982&hilit=p5+maths+questions#p517982
Andy, Ben, Chris shared a box of marbles. Andy received 3/8 od the marbles. Ben
received 3/7 as many marbles as Chris. Andy received 213 more marbles then Ben.
How many marbles were there in the box?

2. Ben: Chris = 3u:7u
Andy: Andy+Ben+Chris = 3:8
Andy: Ben+Chris = 3: 5 = 6u : 10u (total 16u)
Andy: Ben : Chris = 6u: 3u : 7u
So 6u-3u = 3u= 213, 1u = 213/3 = 71
Total 16u = 16 x 71 = 1136 marbles.
1) There are 85 plates of fried noodle for 80 people. Each adult eats 2 plates
of fried noodle and every three children share 1 plate of fried noodle. How many
adults and children are there?
2) 20 boys and girls sold tickets for a funfair. Each ticket was sold at $5.Each
boy sold 5 tickets and each girl sold 3 tickets. The amount collected by the
boys was $20 more than the amount collected by the girls. Find a) how many girls
were there in the group b) how many tickets were sold altogether?
3) Daniel has $160 more than Alex. After giving 1/10 of his money to Alex, he
now has 3 times as much money than Alex. How much money do they have in the
first place?
can be solved by algebra, model or guess and check. The last method should be
least encouraged at this level.
35 adults, 45 children.
Q2 by ratio should be easy enough
8 boys and 12 girls
Q3 by model
Daniel : $200, Alex : $40
Q2 :
# tickets sold by 1 boy : # tickets sold by 1 girl
= 5: 3
ticket sales by 1 boy : ticket sales by 1 girl ( x $5 / ticket)
= 25 : 15
If there are u number of boys,
ticket sales by boys : ticket sales by girls
= 25u : 15 (20 -u)
Difference in ticket sales = 20
25u - 15(20-u) = 20
40u = 320
u = 8
# boys = 8; # girls = 12
Q3 :
Not sure how to draw model here. Need to have before and after model.
Before :
Daniel : 10 units + $160
Alex : 10 units
After :
Daniel : 3 parts

3. Alex : 1 part
Since Daniel gives 1/10 to Alex, he has given (1 unit + $16) to Alex
In the "After" model,
1 part (for Alex) = 11 units + $16
3 parts (for Daniel) = 9 units + $144 ; ie. 1 part for Daniel is 3 units + $48
The difference is 2 parts : this is the key
2(11units + 16) = 6 units + $96
22 units + $32 = 6 units + $96
16 units = $64
1 unit = $4
At first,
Alex has 10 units = 10 X $4 = $40
Daniel has 10 units + $160 = $40 + $160 = $200.
Q1) There are 85 plates of fried noodle for 80 people. Each adult eats 2 plates
of fried noodle and every three children share 1 plate of fried noodle. How many
adults and children are there?
Solution:
---------------Easiest and fastest to solve by algebra.
Let no. of adults be x and no. of children be y
x + y = 80
=> x = 80 -y
2x + 1/3y = 85
2(80-y) + 1/3y = 85
Solve for y and x.
x = 35, y - 45
Q1) There were some marbles at a shop. The ratio of the number of red marbles to
the number of blue marbles was 2:3. When 50 more red marbles and 30 more blue
marbles were added, the ratio of the number of red marbles to the number of blue
marbles became 5:6. How many marbles were there at first?
Solution:
-------------Before adding:
Red : Blue
= 2: 3
= 4: 6
After adding, (based on the above ratio)
Red : Blue
= 4u+50 : 6u+30
= 4u+50 : 6(u+5)
The given ratio, after adding is :
Red : Blue
= 5:6
Compare blue ratio, 6(u+5) = 6
hence, red ratio = 5(u+5)

4. Equate this to the red ratio found earlier.
5(u+5) = 4u+50
5u+25 = 4u +50
u = 25
At first ,
red marbles = 4u = 4 x 25 = 100
blue marbles = 6u = 6 x 25 = 150
2) Susan went shopping with a sum of money. She spent 0.5 of her money plus $5
on a handbag. She then spent 0.5 of the remaining money plus $3 on a pair of
sunglasses. Finally she spent 0.5 of what was left plus $2 on an umbrella. She
was then left with $1.50. How much money did she have at first?
This one is not difficult, but needs to work from the last part of the question.
Can draw a big bar and divide according to the question to visualize better.
$1.50 -----> (+2) = $3.50 ----> (x2) = $7.00 ---> (+3) = $10 ----> (x2) = $20
----> (+5) = $25 ----> (x2) = $50.
3) There are 600 children in Team A and 30% of them are boys.
There are 400 children in Team B and 60% of them are boys.
After some children are transferred from Team B to Team A, 40% of the children
in Team A and 60% of the children in Team B are boys.
How many children are transferred from Team B to Team A?
This is a tricky one. The key is : The total number of boys before and after the
movement is the same.
Total boys = (30% x 600) + (60% x 400) = 420
Total girls = (70% X 600) + (40% x 400) = 580
Total = 1000
After movement, in team A
Boys : Girls
= 4 : 6
= 2 : 3
In team A, there are 5units of children.
In team B, there will be 1000 - 5 units of children.
Team B ratio,
Boys : Girls
= 6 : 4
= 3 : 2
= 3/5(1000 -5u) : 2/5(1000 -5u)
2u of boys in team A + 3/5(1000 - 5u) of boys in team B = 420
2u + 600 - 3u = 420
1u = 180
# of boys in team A after movement = 2u = 360
# of girls in team A after movement = 3u = 540
Total in team A = 900.
# of children transferred from team B to team A = 900 - 600 = 300.

5. There were some marbles at a shop. The ratio of the number of red marbles to the
number of blue marbles was 2:3. When 50 more red marbles and 30 more blue
marbles were added, the ratio of the number of red marbles to the number of blue
marbles became 5:6. How many marbles were there at first?
Hi guys,i just mention i am a tutor looking for students right.so here,i will
show u the shortest way to solve this Qn!(call me at 98793276 if interested)
x: red marbles
y:blue marbles
x/y=2/3
(x+50)/(y+30)=5/6
Solving the equation,
3x=2y
6x+300=5y+150-----*
if 3x=2y,(here you times 2 for both side right?)
6x=4y
sub into *
4y+300=5y+150
150=y
y=150
if y=150,
use this formula u have found jus now
3x=2y
3x=2(150)=300
after that,bring 3 over,hence 300 /3=100.
x=100
hence red marbles=100
blue marbles=150
Jane bought some pizzas for her friends. Her girl friends received twice as many
as her boy friends. She has an equal number of girl and boy friends. Each boy
friend ate 4/7 of a pizza and they finished all the pizza given to them.
Each girl friend ate 1/3 of a pizza and they had 8 1/2 pizza left. How many
pizza did Jane buy?
G [][]
B []
4/7 --> 1 u
1/3 --> 1/3 ÷ 4/7 x 1 = 7/12 u
2 - 7/12 = 1 5/12 u --> 8 1/2 pizzas
3 u --> 3 ÷ 1 5/12 x 8 1/2 = 18 pizzas
Jane bought 18 pizzas.
ratio of number of pizzas eaten by boys : number of pizzas eaten by girls
= 4/7 : 1/3
= 12u : 7u
The girls had twice the number of pizzas the boys had, so total number of pizzas
the girls had = 2 x 12u = 24u

6. 24u - 7u = 8.5 pizzas
17u = 8.5 pizzas
1u = 0.5 pizza
Total number of pizza = 12 u + 24u = 36u = 36 x 0.5 = 18 pizzas
In 2008, the enrolement of Jing Tao Primary School was 60% that of Shu Quan
primary School. In 2009, 120 pupils left Shu Quan Primary School. In the end,
the enrolment of Jing Tao Primary School was 80% that of Shu Quan Primary School
in 2009. What was the enrolment of Jing Tao Primary School in 2009 ?
Number of pupils in Jing Tao remained the same in 2008 and 2009.
In 2008, ratio of pupils in Jin Tao : Shu Quan = 3 : 5 = 12u : 20u
In 2009, ratio of pupils in Jin Tao : Shu Quan = 4 : 5 = 12u : 15u
So 20u -15u = 120, 5u = 120, 1u = 24
In 2009, number of pupils in Jin Tao = 12u = 12 x 24 = 288
After saving for a month, 1/5 of Heidi's savings was equal to 3/7 of Joseph's
savings.
After Heidi spent $356 and Joseph saved an additional $428 , they had a n equal
amount in their savings. How much did Heidi and Joseph save together in the
end?"
There were some blue marbles and white marbles in a bag. If 70 blue marbles were
to be removed from the bag, the ratio of the number of blue marbles to the
number of white marbles would be 3:4. If 112 white marbles were to be removed
from the bag instead, the ratio of the no. of blue marbles to the no. of white
marbles would be 8:7. When 48 more blue marbles were to be added into the bag,
what percentage of all the marbles would be blue marbles at last?
B:W
3:4
+70 : -112
8:7
B 21 490 + 896 (3x7, 70x7, 112x8)
W 32 (4x8)
---------------------11u ----1386
1u -----126
3u ----378
4u ----504
378 + 70 + 48 + 504 = 1000
378 + 70 + 48 = 496
496/1000 x 100 = 49.6%
Answer: 49.6%
Hopefully the above help.

7. 24u - 7u = 8.5 pizzas
17u = 8.5 pizzas
1u = 0.5 pizza
Total number of pizza = 12 u + 24u = 36u = 36 x 0.5 = 18 pizzas
In 2008, the enrolement of Jing Tao Primary School was 60% that of Shu Quan
primary School. In 2009, 120 pupils left Shu Quan Primary School. In the end,
the enrolment of Jing Tao Primary School was 80% that of Shu Quan Primary School
in 2009. What was the enrolment of Jing Tao Primary School in 2009 ?
Number of pupils in Jing Tao remained the same in 2008 and 2009.
In 2008, ratio of pupils in Jin Tao : Shu Quan = 3 : 5 = 12u : 20u
In 2009, ratio of pupils in Jin Tao : Shu Quan = 4 : 5 = 12u : 15u
So 20u -15u = 120, 5u = 120, 1u = 24
In 2009, number of pupils in Jin Tao = 12u = 12 x 24 = 288
After saving for a month, 1/5 of Heidi's savings was equal to 3/7 of Joseph's
savings.
After Heidi spent $356 and Joseph saved an additional $428 , they had a n equal
amount in their savings. How much did Heidi and Joseph save together in the
end?"
There were some blue marbles and white marbles in a bag. If 70 blue marbles were
to be removed from the bag, the ratio of the number of blue marbles to the
number of white marbles would be 3:4. If 112 white marbles were to be removed
from the bag instead, the ratio of the no. of blue marbles to the no. of white
marbles would be 8:7. When 48 more blue marbles were to be added into the bag,
what percentage of all the marbles would be blue marbles at last?
B:W
3:4
+70 : -112
8:7
B 21 490 + 896 (3x7, 70x7, 112x8)
W 32 (4x8)
---------------------11u ----1386
1u -----126
3u ----378
4u ----504
378 + 70 + 48 + 504 = 1000
378 + 70 + 48 = 496
496/1000 x 100 = 49.6%
Answer: 49.6%
Hopefully the above help.