SOLUTION: the units digit of a 3 digit number is 5. the sum of its digits is 11. if the units and 100s digits are reversed, the sum of the new number and the original number is 787. find the
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Question 203506: the units digit of a 3 digit number is 5. the sum of its digits is 11. if the units and 100s digits are reversed, the sum of the new number and the original number is 787. find the original number.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
the units digit of a 3 digit number is 5. the sum of its digits is 11.
if the units and 100s digits are reversed, the sum of the new number and
the original number is 787. find the original number.
;
Let x = the 100's digit
Let y = the 10's digit
then
100x + 10y + 5 = original number
:
"the sum of its digits is 11."
x + y + 5 = 11
x + y = 11 - 5
x + y = 6
y = (6-x)
;
"if the units and 100s digits are reversed, the sum of the new number and
the original number is 787."
500 + 10y + x + 100x + 10y + 5 = 787
Group like terms
10y + 10y + x + 100x + 505 = 787
:
101x + 20y = 787 - 505
:
101x + 20y = 282
Substitute (6-x) for y
101x + 20(6-x) = 282
:
101x + 120 - 20x = 282
:
101x - 20x = 282 - 120
:
81x = 162
x =
x = 2
then
y = 6 - 2
y = 4:
:
245 = original number
;
:
Check solution in the statement:
if the units and 100s digits are reversed, the sum of the new number and
the original number is 787.
542 + 245 = 787
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