SOLUTION: the sum of the digit's of a three digit number is 14. If the hundred's and unit's are interchanged the resulting number is 594 more than original but if the ten's and the unit's di
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Question 161275: the sum of the digit's of a three digit number is 14. If the hundred's and unit's are interchanged the resulting number is 594 more than original but if the ten's and the unit's digit are interchanged, the now number is more than the original by 36. Find the number?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the sum of the digit's of a three digit number is 14. If the hundred's and unit's are interchanged the resulting number is 594 more than original but if the ten's and the unit's digit are interchanged, the now number is more than the original by 36. Find the number?
:
The number: 100x + 10y + z
:
"the sum of the digit's of a three digit number is 14."
x + y + z = 14
;
" If the hundred's and unit's are interchanged the resulting number is 594 more than original"
100z + 10y + x - (100x + 10y + z) = 594
100z + 10y + x - 100x - 10y - z = 594
100z - z + 10y - 10y + x - 100x = 594
99z - 99x = 594
Simplify, divide equation by 99
z - x = 6
:
" but if the ten's and the unit's digit are interchanged, the now number is more than the original by 36."
100x + 10z + y - (100x + 10y + z) = 36
100x + 10z + y - 100x - 10y - z = 36
100x - 100x + 10z - z + y - 10y = 36
9z - 9y = 36
Simplify divide by 9
z - y = 4
:
Find the number?
:
Arrange all three equation for elimination
x + y + z = 14
-x+ 0 + z = 6
0 - y + z = 4
----------------adding eliminates x and y, find z
0 + 0 +3z = 24
z =
z = 8
:
Find x:
z - x = 6
8 - x = 6
x = 2
:
Find y:
z - y = 4
8 - y = 4
y = 4
:
The number = 248
:
Check solution in the statement:
"If the hundred's and unit's are interchanged the resulting number is 594 more than original"
842 - 248 = 594
:
YOu can check the solutiona in the other statements
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