Name : ____________________ Date : _____________
Score : _____________
Write down your correct answer and show your workings:
1) David had 2 bags
of marbles. After he had sold 44 marbles from Bag X to his friend,
the number of marbles in Bag Y
was 5/7 of the number of marbles in Bag X.
Given that there were 2/5 as many marbles in Bag Y as in Bag X originally,
find the number of marbles in Bag X at first.
2) John read a book
in 3 days. He read 35% of the total number of pages in the book on the
2nd day.
The ratio of the total number of pages of book he read on the 1st and 2nd
day to the number of pages he read on the
3rd day was 11:9. If he had read 75 more pages on the 3rd day than on the
1st day, how many pages of the book did
he read on the 2nd day ?
3) 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?
4) 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?
5) 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?
Answers:
1)
2)
3)
# 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
4)
Before :
Daniel : 10 units + $160
Alex : 10 units
After :
Daniel : 3 parts
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.
5)
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