SOLUTION: The sum of the digits of a two digit number is 10. The number formed by reversing the number is 4 less than 5 times the number. Find the original number? Can you please help me

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Question 691413: The sum of the digits of a two digit number is 10. The number formed by reversing the number is 4 less than 5 times the number. Find the original number?
Can you please help me out with this question I really don't understand? thanks in advance
Found 2 solutions by josmiceli, stanbon:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the tens digit = +a+
Let the units digit = +b+
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The number looks like ab, like the number 36,
but the value of the number is +10a+%2B+b+,
the same way that +36+=+3%2A10+%2B+6+
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given:
(1) +a+%2B+b+=+10+
This is just talking about the digits and not the value
of the number
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The VALUE of the number, as I said, is +10a+%2B+b+
and the value of the number formed by reversing the digits is
+10b+%2B+a+
You are told that
(2) +10b+%2B+a+=+5%2A%28+10a+%2B+b+%29+-+4+
You have 2 equations, (1) and (2), and 2 unknowns, so
it is solvable.
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(2) +10b+%2B+a+=+50a+%2B+5b+-+4+
(2) +5b+=+49a+-+4+
and
(1) +a+%2B+b+=+10+
(1) +b+=+10+-+a+
Substitute (1) into (2)
(2) +5b+=+49a+-+4+
(2) +5%2A%28+10+-+a+%29+=+49a+-+4+
(2) +50+-+5a+=+49a+-+4+
(2) +54a+=+54+
(2) +a+=+1+
and, since
(1) +b+=+10+-+a+
(1) +b+=+10+-+1+
(1) +b+=+9+
The number is 19
check answer:
(2) +10b+%2B+a+=+5%2A%28+10a+%2B+b+%29+-+4+
(2) +10%2A9+%2B+1+=+5%2A%28+10%2A1+%2B+9+%29+-+4+
(2) +91+=+5%2A19+-+4+
(2) +91+=+95+-+4+
(2) +91+=+91+
OK




Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of the digits of a two digit number is 10. The number formed by reversing the number is 4 less than 5 times the number. Find the original number?
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Let the number be 10t+u ; t is the 10's digit; u is units digit
The reverse number is 10u + 5
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Equations:
t + u = 10
-------
10u+t = 5(10t+u)-4
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Simplify the bottom equation:
10u+t = 50t+5u-4
49t - 5u = 4
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Substitute for t = 10-u for "t" and solve for "u":
49(10-u) - 5u = 4
490 - 54u = 4
54u = 486
u = 9
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Now, solve for "t" using t + u = 10
---
t+9 = 10
t = 1
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The number is 10t+u = 10*1 + 9 = 19
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Cheers,
Stan H.
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