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[Adele Yeo]

2) Concept: Constant difference (Ratio)


The ratio of Martin's age to Jeremy's age is 1:4. In 15 years time, the new ratio is 2:3. How old is Martin now?

Note: The age difference/ age gap always remain the same.
Thus, we have to make both difference the same.
1:4 (difference is 3 units)
2:3 = 6:9 (multiply by 3 to have the difference of 3 units)

Difference:
Martin: 1 unit to 6 units (Diff: 5u)
Jeremy: 4 units to 9 units (Diff: 5u)
Thus, the 5 units will be the growth of 15 years
5 units => 15
1 unit => 3
Martin is 3 years old now.

[jwxh]

besides guess and check, what is the shortcut solution for below question. tks


A stapler cost $8. A dictionary cost $12.50. Tom bought 9 staplers and dictionaries. He paid $31 more for the staplers than the dictionaries. How many dictionaries did tom buy?

[Adele Yeo]

Hi jwxh,


Thank you for the qn. I welcome more questions

A stapler cost $8. A dictionary cost $12.50. Tom bought 9 staplers and dictionaries. He paid $31 more for the staplers than the dictionaries. How many dictionaries did tom buy?[/quote]


Method 1: Algebra
Let the number of stapler be x. Let the number of dictionary be y.
Equation 1: x + y =9
Equation 2: 8x - 12.5y = 31

From eqn 1, we can say that x = 9 - y
Then we substitute x = 9 - y into eqn 2.
8 (9 - y) - 12.5y = 31
72 - 8y - 12.5y = 31
12.5y + 8y = 72 - 31
20.5y = 41
y = 2
Thus, he bought two dictionaries.

Method 2: Assumption method
Assume that Tom has spent all his money on staplers
9 x $8 = $72

Take out the $31 more that he spent on staplers
$72 - $31 = $41

Now we can add up the amount of a stapler and a dictionary
$12.50 + $8 = $20.50 (1 set of stapler and dictionary)

Divide
$41 / $20.50 = 2
Thus, he bought two dictionaries.


EXAM TIPS: If you have time, you can check the answer.
Dictionary: 2 x $12.50 = $25
Staplers: 7 x 8 = $56
Difference: $56 - $25 = $31

[Adele Yeo]

Concept: Repeated Identity


Mary and Jenny had a number of stickers in the ratio 4: 1. Jenny and Grace had a number of stickers in the ratio 2: 3. If they have a total of 169 stickers altogether, how many stickers does Mary have?

Exam tips!!
1. Highlight the key words
2. Identify the concept: Repeated identity
3. Write down the info provided in the question

Whose name is repeated twice? JENNY!!
M : J
4 : 1 (multiply by 2 to make Jenny's ratio the same)

J : G
2 : 3

Put the ratio together to compare
M : J : G
8 : 2 : 3
Total units = 8 + 2 + 3 = 13

13 units -> 169 stickers
1 unit -> 13 stickers
8 units -> 104 stickers
Mary has 104 stickers

** Repeated identity questions can be in the form of percentages, fractions and ratio.

[Adele Yeo]

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