mathematics different stretegies3

7/28/2019 Mathematics Different Stretegies3

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Question:The sum of the digits of a two-digitnumber is 14. If the digits arereversed, the number is increasedby 18. What is the number?


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Solution

1st strategy :Using substitution

Let T = tens-digit, let U= units-digit

The sum of digits is 14, so equation is U+T = 14 ----

The two-digit number is : 10T+U Reverse digits : 10U + T

This is 18 more than original number.

So, 10U+T=(10T+U)+18

Simplifies 9U 9T =18 U T =2 ---- + : 2U=16 U=8 ----

Sub into : 8+T=14 T=6

So, the two-digit number is 68


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2ndstrategy :

Using guess and check

If choose 5 , 9

Sum of digits is 5+9=14

But 95 - 59 = 36 , when the digits reversed, it is increasedby 36, so it is wrong.

If choose 6 , 8Sum of digits is 6+8 = 14

86 68 = 18 , when the digits reversed, it is increased by18 too, it is correct answer.


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3rdstrategy

Construct a table

Digits selected Sum of digits Difference of numberwhen digits reversed

5 , 9 5+9 = 14 95 -59 = 36

6 , 8 6+8 = 14 86-68 = 18


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Question :Ms.Jessy went to a store, spent half ofher money and then $10 more. She

went to a second store, spent half ofher remaining money and then $10more. But she had no money left. Howmuch money did she have to being

with?


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Solution1st strategy :

Using algebraic expression Let x be the amount of money she have bring at the

beginning The equation for the first store :

x- x -10= what she had left after the first store The equation for what was left after the second store :(what she had left after the first store *0.5) -10 = $0so((x- x -10)*0.5)-10 = 0(x- x -10) = 10x- x -10 = 20x- x = 30x = 30x = 60She started with $60.


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2ndstrategy :

Guess and checkAt the beginning At the 1st store At the 2nd store

$100 ($100/2)-$10

=$50-$10=$40

($40/2)-$10

=$20-$10=$10

$80 ($80/2)-$10=$40-$10

=$30

($30/2)-$10=$15-$10

=$5$60 ($60/2)-$10

=$30-$10=$20

($20/2)-$10=$10-$10=$0


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3. In a sports club with 30 members,17 play badminton and 19 playtennis and 2 do not play either.How many members play both

badminton and tennis?


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1st

StrategyUsingVenn diagram,

In a sports club with 30 members,there are 2 membersdoes not play either.

Members involve in playing badminton and tennis

=30-2

=28 members

Members who play both badminton and tennis=(17+19)-28

=36-28

=8 members


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17

Badminton

19

Tennis8

28


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2nd

StrategyUsing algebraic expression,

In a sports club with 30 members,there are 2 members

does not play either. Members involve in playing badminton and tennis

=30-2

=28


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Let members who play both be n.

Hence, badminton players = (17 - n)

tennis players = (19 - n) 28 = (17 - n) + (19 - n) + n

28 = 36-2n+n

28=36-n

n=36-28

n=8 members


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3rd

strategy By using drawing the pictures,

There are 30 members, but 2 of them do not play both

badminton and tennis. OOOOOOOOOO

OOOOOOOOOO

OOOOOOOOOO

So there are 28 members who play both badmintonand tennis.


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That means the O picture more than 28 is the memberswho play both badminton and tennis.

Lets count it,

19+17=36OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

the numbers of red colour O is 8. Hence, there are 8 members who play both badminton and

tennis.


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4th

strategy Using guess and check

Badminton Tennis Both Does not

play

Total

15 17 2 2 36

13 15 4 2 34

11 13 6 2 32

9 11 8 2 30

mathematics different stretegies3

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