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Question 1043320: A number consists of two digits, the digits in the ten’s place exceeds that in the unit’s place by 5 and if 5 times the sum of the digits be subtracted from the number, the digits will be reversed. Find the number.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! let a = the 10's digit
let b = the units
:
Write an equation for each statement
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A number consists of two digits, the digits in the ten’s place exceeds that in the unit’s place by 5
a = b + 5
and if 5 times the sum of the digits be subtracted from the number, the digits will be reversed.
10a + b - 5(a+b) = 10b + a
10a + b - 5a - 5b = 10b + a
combine a's on the left, b's on the right
10a - 5a - a = 10b - b + 5b
4a = 14b
simplify, divide by 2
2a = 7b
from the 1st statement, replace a with (b+5)
2(b+5) = 7b
2b + 10 = 7b
10 = 7b - 2b
10 = 5b
b = 10/5
b = 2
then
a = 2 + 5
a = 7
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72 is our number
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Check solution in the 2nd statement
72 - 5(7+2) = 27
72 - 45 = 27
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