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Question 972441: Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the two digits is 3, find the number.
Plzzzzzz solve it.......
Thank you. ...!!!!
Found 3 solutions by rothauserc, Edwin McCravy, MathTherapy:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! let xy be the two digit number, now
xy = 10x + y and
x - y = 3 then
x = y+3
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7(xy) = 4(yx)
7(10x+y) = 4(10y+x)
now substitute y+3 for x
7(10(y+3)+y) = 4(10y+y+3)
7(10y+30+y) = (40y+4y+12)
77y+210 = 44y+12
33y = -198
y = -6
x = -3
xy = -36
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check answer
7(-36) = 4(-63)
-252 = -252
answer checks
Answer by Edwin McCravy(20055)  (Show Source):
You can put this solution on YOUR website!
The other tutor is technically correct because he interpreted "the difference
of the digits" as "the first digit minus the second digit". However I think
your teacher meant the ABSOLUTE DIFFERENCE, "larger minus smaller", rather
than "first-second", as "difference" is usually taken. This shows a difficulty
in semantics that we run into in mathematics.
The tens digit = t
The units digits = u
The two-digit number = (10t+u)
The number obtained by reversed = (10u+t)
Seven times a two digit number is equal to four times the number obtained by reversing the digits.
Replace the words "a two digit number" by (10t+u)
Replace the words "the number obtained by reversing the digits" by (10u+t).
Then the above sentence becomes
Seven times (10t+u) is equal to four times (10u+t).
Replace the words "Seven times" by "7*"
Replace the words "four times" by "4*"
Replace the words "is equal to" by "=":
7(10t+u) = 4*(10u+t)
Simplify:
70t+7u = 40u+4t
66t = 33u
Divide both sides by 33
2t = u
>>...the difference between the two digits is 3,...<<
I am interpreting this as ABSOLUTE difference. So we have to make sure
that we take the smaller digit away from the larger digit. We can tell
by 2t = u that the units digit u is larger because it equals twice what
the tens digit equals. so
LARGER DIGIT - SMALLER DIGIT = 3
u - t = 3
So we have the system of equations:
From the first equation, we substitute 2t for u in the second equation:
u-t = 3
2t-t = 3
t = 3
Substitute in either equation of the system:
2t = u
2(3) = u
6 = u
Since the tens digit is t=3 and the units digit is u=6,
the number is 36
Checking:
Seven times a two digit number, 36, which gives 7×36=252
is equal to four times the number obtained by reversing the digits, 63,
which gives 4×63 = 252.
That checks.
the (ABSOLUTE) difference between the two digits is 3, 6-3 = 3,
So it checks.
Edwin
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Seven times a two digit number is equal to four times the number obtained by reversing the digits. If the difference between the two digits is 3, find the number.
Plzzzzzz solve it.......
Thank you. ...!!!!
Let the tens and units digits be T and U, respectively
Then original number is: 10T + U
Reversed number is: 10U + T
Seven (7) times the original number is (=) ONLY 4 times the reversed number, which suggests that the
original number is SMALLER than the reversed number. As the original number is SMALLER than the reversed
number, U, or the units digit is LARGER than the tens digit. Therefore, we get the following system of equations:
7(10T + U) = 4(10U + T)
U – T = 3
Solve this system for T: the tens digit, and U: the units or ones digit. You'll then have the ORIGINAL NUMBER.
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