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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