SOLUTION: five times the units digit of a two-digit number equals 4 more than the tens digit. If the digits are reversed, the new number is 5 less than half the original number. Find the nu
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Question 923441: five times the units digit of a two-digit number equals 4 more than the tens digit. If the digits are reversed, the new number is 5 less than half the original number. Find the number.
email address is sundaeaw@yahoo,com 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
then
10a+b = "the original number"
and
10b+a = "the reversed number"
:
Write an equation for each statement
:
five times the units digit of a two-digit number equals 4 more than the tens digit.
5b = a + 4
rearrange for substitution
a = 5b - 4
:
If the digits are reversed, the new number is 5 less than half the original number.
10b + a = (10a+b) - 5
multiply both sides by 2 to get rid of the fraction, you then have
20b + 2a = 10a + b - 10
20b - b = 10a - 2a - 10
19b = 8a - 10
replace a with (5b-4), from the 1st statement
19b = 8(5b-4) - 10
19b = 40b - 32 - 10
19b = 40b - 42
42 = 40b - 19b
42 = 21b
b = 42/21
b = 2 is the units digit
then we now a = 5b-4
a = 5(2) - 4
a = 10 - 4
a = 6 is the 10's digit
:
62 is the original number
:
Check this out in the statement:
"If the digits are reversed, the new number is 5 less than half the original number."
26 = (62) - 5
26 = 31 - 5
