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Who Can Please Help Solve THIS Question......??? by toms55(m): 9:16pm On Sep 01, 2015
Just arrived home and my little sister gave me this baths questions to help her solve, after racking my brain I was unable to help her solve them. Who can help?...



(1) the difference between the digits of a two-digit number is 1. The number itself is 1 more than 5 times the sum of bits digits. If the unit digit is greater than the digit, find the number.





(2) In a positive number of two digits, the sum of the digit is 15. If the digits are interchanged, the number is increased by 9. Find the number.
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 9:17pm On Sep 01, 2015
embarassed
Re: Who Can Please Help Solve THIS Question......??? by ladyF(f): 9:18pm On Sep 01, 2015
87 is the second.
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 9:22pm On Sep 01, 2015
ladyF:
87 is the second.
I need the solution fully explained mathematically please embarassed.... show the working please
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 9:26pm On Sep 01, 2015
The first is 56

The second is 78.

I used deductive deductive reasoning to quickly find the answer and post it. However, if you still can't solve it, I will post a mathematical working.
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 9:28pm On Sep 01, 2015
Teempakguy:
The first is 56

The second is 78.

I used deductive deductive reasoning to quickly find the answer and post it. However, if you still can't solve it, I will post a mathematical working.
. Please do, I need the workings.. thanks and God bless
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 9:30pm On Sep 01, 2015
toms55:
. Please do, I need the workings.. thanks and God bless
okay, give me a few minutes.

1 Like

Re: Who Can Please Help Solve THIS Question......??? by Nobody: 9:33pm On Sep 01, 2015
Yh, for the first its 56
How?
-difference btw 5 nd 6 is 1. Sarisfies the first condition
The, 5 multiplied by each af 5 and 6 gives you. 25 and 30 , totalling 55 then +1. gives back 56. QED!


Leh me do the second one too abi?
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 9:35pm On Sep 01, 2015
Sabrwahaqqo:
Yh, for the first its 56
How?
-difference btw 5 nd 6 is 1. Sarisfies the first condition
The, 5 multiplied by each af 5 and 6 gives you. 25 and 30 , totalling 55 then +1. gives back 56. QED!


Leh me do the second one too abi?
I'm not a guru in mathematics, it is a simultaneous equation question, so I'm not really sure ..
Thanks for helping out
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 9:39pm On Sep 01, 2015
Yh the second is 87

The sum is 15 ..yeah
Then if interchanged ,you have 78
Mind you it follows that numerically you have number in the order 7,8,9. So , it increases by 9 like that wink
But the real number before interchanging is 87 so, 78 will be wrong


This is more af logical reasoning mehn, nat Maths ... Well, QED!
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 9:52pm On Sep 01, 2015
Sabrwahaqqo:
Yh the second is 87

The sum is 15 ..yeah
Then if interchanged ,you have 78
Mind you it follows that numerically you have number in the order 7,8,9. So , it increases by 9 like that wink
But the real number before interchanging is 87 so, 78 will be wrong


This is more af logical reasoning mehn, nat Maths ... Well, QED!
well, yeah . . . but his sisters teacher doesn't care about that, does she? cheesy cheesy

Also, I beg to disagree. Note that it does not increase TO nine but BY nine.
This implies that if we are to find a number whose digits will be interchanged by adding nine to it.
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 9:56pm On Sep 01, 2015
Teempakguy:
well, yeah . . . but his sisters teacher doesn't care about that, does she? cheesy cheesy

Also, I beg to disagree. Note that it does not increase TO nine but BY nine.
This implies that if we are to find a number whose digits will be interchanged by adding nine to it.
I'm still waiting for the workings
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:03pm On Sep 01, 2015
embarassed
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:09pm On Sep 01, 2015
embarassed
toms55:
embarassed
.... x+y......(1)
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 10:10pm On Sep 01, 2015
The second.

x + y = 15. . . . . {1}. Because their sum is 15.

10x + y + 9 = 10y + x . . . {2}. Because their place values are switched upon the addition of nine.

From {1}

y = 15 - x . . . . {3}

Substituting, this into {2}

10x + (15 - x) + 9 = 10(15 - x) + x

Tidying the above mess up, [first open the bracket on the right hand side before anything. Add like terms.]

9x + 24 = 150 - 9x

Collect them like terms.

18x = 126

Divide both sides by 18.

x = 7

Substitute 7 for x in {3} to get y and . . . . we're done here.

Well, after getting x and y, we know from our place values that they form a two digit number.
This means that the number is 10 x 7 + 8 = 78

The other loading,

Bros, I can't do anything too much o . . . this is your sister's home work for crying out loud nah. Even what I am doing now is a lil illegal. embarassed
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 10:11pm On Sep 01, 2015
Teempakguy:
well, yeah . . . but his sisters teacher doesn't care about that, does she? cheesy cheesy

Also, I beg to disagree. Note that it does not increase TO nine but BY nine.
This implies that if we are to find a number whose digits will be interchanged by adding nine to it.

We did logical reasoning when I was in the primaries and junior high anyway.. Might be that this isn't , aint sure grin ....And yes, all these can be summed up algebraically beht mahn, no pen here and no time tongue


Man, Even if !!! The sequence 8, 7 doesn't increase by 9 ... 7,8 does !

Like this follows NOT tha fixed mathematical language like say; divide 4 by 2 or 2 by 4 where you'll af course be getting two different answers .. Tis simple English all through mehn . #standing to be corrected tho !
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:17pm On Sep 01, 2015
Teempakguy:
The second.

x + y = 15. . . . . {1}. Because their sum is 15.

10x + y + 9 = 10y + x . . . {2}. Because their place values are switched upon the addition of nine.

From {1}

y = 15 - x . . . . {3}

Substituting, this into {2}

10x + 15 - x + 9 = 10(15 - x) + x

Tidying the above mess up, [first open the bracket on the right hand side before anything. Add like terms.]

9x + 24 = 150 - 9x

Collect them like terms.

18x = 126

Divide both sides by 18.

x = 7

Substitute 7 for x in {3} to get y and . . . . we're done here.

The other loading,





Thanks but is the answer not 78?.. not clear, please add all the brackets and less explanation, lemme just as her to copy the solution, and the explanation is left to her teacher
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 10:22pm On Sep 01, 2015
toms55:


Thanks but is the answer not 78?
Yes Na.

10x + y

x = 7, y = 8

This is 10(7) + (cool = 78
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:33pm On Sep 01, 2015
Teempakguy:
The second.

x + y = 15. . . . . {1}. Because their sum is 15.

10x + y + 9 = 10y + x . . . {2}. Because their place values are switched upon the addition of nine.

From {1}

y = 15 - x . . . . {3}

Substituting, this into {2}

10x + (15 - x) + 9 = 10(15 - x) + x

Tidying the above mess up, [first open the bracket on the right hand side before anything. Add like terms.]

9x + 24 = 150 - 9x

Collect them like terms.

18x = 126

Divide both sides by 18.

x = 7

Substitute 7 for x in {3} to get y and . . . . we're done here.

Well, after getting x and y, we know from our place values that they form a two digit number.
This means that the number is 10 x 7 + 8 = 78

The other loading,

Bros, I can't do anything too much o . . . this is your sister's home work for crying out loud nah. Even what I am doing now is a lil illegal. embarassed






bros haba, lets help this little girl out abeg...
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:37pm On Sep 01, 2015
uote author=Teempakguy post=37575332]The second.

x + y = 15. . . . . {1}. Because their sum is 15.

10x + y + 9 = 10y + x . . . {2}. Because their place values are switched upon the addition of nine.

From {1}

y = 15 - x . . . . {3}

Substituting, this into {2}

10x + (15 - x) + 9 = 10(15 - x) + x

Tidying the above mess up, [first open the bracket on the right hand side before anything. Add like terms.]

9x + 24 = 150 - 9x

Collect them like terms.

18x = 126

Divide both sides by 18.

x = 7

Substitute 7 for x in {3} to get y and . . . . we're done here.

Well, after getting x and y, we know from our place values that they form a two digit number.
This means that the number is 10 x 7 + 8 = 78

The other loading,






[/quote] please can you explain how you get the bolded
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 10:47pm On Sep 01, 2015
Since the unit is greater than the ten.

y - x = 1 . . . . . . 1

10x + y = 5(x + y) + 1 . . . . . . . 2

10x + y = 5x + 5y + 1

From 1, y = x + 1 . . . . . . 3

10x + (x + 11) = 5x + 5(x + 1) + 1

11x + 1 = 5x + 5x + 5 + 1

Collect like terms.

x = 5

replace in 3.

y = x + 1
y = 5 + 1
y = 6

Combining this,

The digit is 56.
Re: Who Can Please Help Solve THIS Question......??? by Germaine324(f): 10:48pm On Sep 01, 2015
I can only solve no two very well. My number is also based on assumption
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:49pm On Sep 01, 2015
Teempakguy:
Since the unit is greater than the ten.

y - x = 1 . . . . . . 1

10x + y = 5(x + y) + 1 . . . . . . . 2

10x + y = 5x + 5y + 1

From 1, y = x + 1 . . . . . . 3

10x + (x + 11) = 5x + 5(x + 1) + 1

11x + 1 = 5x + 5x + 5 + 1

Collect like terms.

x = 5

replace in 3.

y = x + 1
y = 5 + 1
y = 6

Combining this,

The digit is 56.

wow I'm just so overwhelmed.. in fact "thank you" is an understatement.

God bless you
Re: Who Can Please Help Solve THIS Question......??? by Germaine324(f): 10:50pm On Sep 01, 2015
If x is the first digit and y is the second digit ; x+y =15
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:54pm On Sep 01, 2015
toms55:
uote author=Teempakguy post=37575332]The second.

x + y = 15. . . . . {1}. Because their sum is 15.

10x + y + 9 = 10y + x . . . {2}. Because their place values are switched upon the addition of nine.

From {1}

y = 15 - x . . . . {3}

Substituting, this into {2}

10x + (15 - x) + 9 = 10(15 - x) + x

Tidying the above mess up, [first open the bracket on the right hand side before anything. Add like terms.]

9x + 24 = 150 - 9x

Collect them like terms.

18x = 126

Divide both sides by 18.

x = 7

Substitute 7 for x in {3} to get y and . . . . we're done here.

Well, after getting x and y, we know from our place values that they form a two digit number.
This means that the number is 10 x 7 + 8 = 78

The other loading,






please can you explain how you get the bolded
bros abeg no forget the bolded
Re: Who Can Please Help Solve THIS Question......??? by Germaine324(f): 10:54pm On Sep 01, 2015
As the number is two digits then am going to say, 10x( if it were three digits twould have been 100)
Equation one will therefore be; 10x + y=z
Reversing, Equation two will be; x+10y= z+9
All these assuming the unknown number is z
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:55pm On Sep 01, 2015
Teempakguy:
Since the unit is greater than the ten.

y - x = 1 . . . . . . 1

10x + y = 5(x + y) + 1 . . . . . . . 2

10x + y = 5x + 5y + 1

From 1, y = x + 1 . . . . . . 3

10x + (x + 11) = 5x + 5(x + 1) + 1

11x + 1 = 5x + 5x + 5 + 1

Collect like terms.

x = 5

replace in 3.

y = x + 1
y = 5 + 1
y = 6

Combining this,

The digit is 56.

bros abeg no forget the bolded in the first solution
Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 10:56pm On Sep 01, 2015
Germaine324:
As the number is two digits then am going to say, 10x( if it were three digits twould have been 100)
Equation one will therefore be; 10x + y=z
Reversing, Equation two will be; x+10y= z+9
All these assuming the unknown number is z
Thanks so much
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 10:57pm On Sep 01, 2015
please can you explain how you get the bolded

10x + 15 - x + 9 = 10(15 - x) + x

Add the terms on the Left Hand Side and open the bracket on Right Hand Side.

9x + 24 = 150 - 10x + x

Add the terms on the Right Hand Side.

9x + 24 = 150 - 9x


QED
Re: Who Can Please Help Solve THIS Question......??? by Nobody: 11:00pm On Sep 01, 2015
toms55:
wow I'm just so overwhelmed.. in fact "thank you" is an understatement.

God bless you
you're welcome. cheesy cheesy

Look above. I have already treated the bolded.

1 Like

Re: Who Can Please Help Solve THIS Question......??? by Germaine324(f): 11:01pm On Sep 01, 2015
From eqn two; x+10y= z+9
X + 10y-9=z
Substitute eqn one in two;
10x+ y=x+10y-9
10x-x=10y-y-9
9x=9y-9
;x-y=-1 or x= y-1

1 Like

Re: Who Can Please Help Solve THIS Question......??? by toms55(m): 11:02pm On Sep 01, 2015
Thanks @ all

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