SOLUTION: The sums of the digits of a two digit number is 14. If 4 is added to the number, the result is seven times the units digit. find the number?
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-> SOLUTION: The sums of the digits of a two digit number is 14. If 4 is added to the number, the result is seven times the units digit. find the number?
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Question 695813: The sums of the digits of a two digit number is 14. If 4 is added to the number, the result is seven times the units digit. find the number?
I have tried solving this problem like 15 times and i still have't come up with the correct answer please help me understand how to do this problem and how to write the equation Found 2 solutions by ankor@dixie-net.com, josmiceli:Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! let t = the ten's digit
let u = the units
then
10t + u = "the number"
:
Write an equation for each statement:
:
"The sums of the digits of a two digit number is 14."
t + u = 14
u = (14-t); we can use this form for substitution
:
"If 4 is added to the number, the result is seven times the units digit."
(10t+u) + 4 = 7u
10t + 4 = 7u - u
10t + 4 = 6u
replace u with (14-u) from the 1st statement equation
10t + 4 = 6(14-t)
10t + 4 = 84 - 6t
10t + 6t = 84 - 4
16t = 80
t = 80/16
t = 5 is the 10's digit
then
14 - 5 = 9 is the units
:
59 is the number
:
:
Confirm this in the 2nd statement;
"If 4 is added to the number, the result is seven times the units digit."
4 + 59 = 7(9)
:
Was this understandable for you?
You can put this solution on YOUR website! Call the tens digit of the number
Call the units digit of the number
given:
(1)
(2)
( note that "the number" is actually )
--------------
(2)
Multiply both sides of (1) by , , and
add the equations
(1)
(2)
and, since
(1)
(1)
(1)
The number is 59
check:
(2)
(2)
(2)
(2)
OK
