'Set' Question

Question: 



Solution:

It can be solved using 'set'

1 set --> 8 bags of sweets and 1 bag of chocolate
Money collected for 1 set --> 8 x 5.5 + 2 = 46
No. of sets = 3128 / 46 = 68

No. of sweets sold --> 68 x 8 x 4 = 2176
No. of chocolates sold --> 68 x 8 = 544

Another Model Question

Question: 

Alex, Ben and Caleb had some stamps. Alex had 90 stamps more than Ben, and Ben had 10 stamps more than Caleb. After Alex had given Ben 95 of his stamps and Caleb bought some stamps, Alex and Caleb had the same number of stamps while Ben had thrice as much as either of them.

a) How many stamps did Caleb have at first?
b) How many stamps did they have altogether at first?

Solution:

Working Backwards

A fraction question sent in by Mr Chiow

Solution:

In the end: Z = L à 174 

After L gave 2/5, she had 3 units left.

So 3u à 174

1u à 58

Z received 2u from L, so Z originally had 174 – 2u à 174 – 116 = 58

Before L gave 2/5, she had 5 units. 5u à 290

Z had 58 after he gave 1/3, 2u à 58, 1u à 29 (given to L)

L had 290 after she received 29

L at first à 290 – 29 = 261 

Another common question on Ratio and Age

Question:

The ratio of the age of Mdm Huda to her son's age is 5:1 now. In 7 years time, she would be thrice as old as her son. What is the total age of Mdm Huda and her son now?

Solution:

Before ratio --> H : S = 5 : 1 (difference 4u)
After ratio --> H : S = 3 : 1 (difference 2u)
Age difference between Mdm Huda and her son is unchanged after 7 years

So make the difference same
After ratio (x2) --> H : S = 6 : 2 (difference 4u now, same as before)
1u (6u-5u) --> 7 years
Age of Mdm Huda now is 5u --> 5x7=35
Age of her son now is 1u --> 7

Two Math Questions

Two questions from Belnanna:

Question 1:

In a school science fair, there were exhibits from class A , class B and class C. Altogether, 25 exhibits came from class B and class C. In a total of 16 exhibits were not from class C and a total of 15 exhibits were not from class B.
How many exhibits were there altogether?

Solution:

16 exhibits not from C --> A + B = 16
15 exhibits not from B --> A + C = 15
2A + B + C = 31
B + C = 25
2A --> 6
A --> 3
B --> 13
C --> 12
Total exhibits --> 3 + 13 + 12 = 28


Question 2:

The length of a rectangular pond is 14 m and its breadth is 7 m. Fatimah wants to build a running path around the pond. The width of the path is 1/2 m. what is the area of the running path?

Solution:

Units and parts

Question:

Class 5A and 5B have the same number of pupils. The ratio of the number of boys in 5A to the number of boys in 5B is 2 : 3. The number of girls in 5A to the number of girls in 5B is 7 : 4. 
(A) Find the ratio of the number of boys to the number of girls in 5A.
(B) If there are 15 fewer girls than boys in 5B, how many pupils are there in 5B?

Solution:

5A boys : 5B boys = 2u : 3u
5A girls : 5B girls = 7p : 4p

5A and 5B same no. of pupils --> 2u + 7p = 3u + 4p --> 1u = 3p
5A boys : 5B boys = 2u : 3u = 6p : 9p

(A) 5A boys : 5A girls = 6 : 7

(B) 5B boys : 5B girls = 9 : 4 
5parts --> 15 
1p --> 3
No. of pupils in 5B is 13p --> 13 x 3 = 39

Cross Method for Fraction / Ratio Questions

Here is a question from visitor Belnanna:

There were 3/5 as many children as adults on a bus. At the next stop, 3 children boarded and 2 adults alighted from the bus.Then, there were 5/6 as many children as adults on the bus. How many children were there on the bus at first.

Solution: