SOLUTION: The some of a digit is 8. If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.
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Question 137560: The some of a digit is 8. If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.
The some of the digits is 8. The number 16 is less than the product of 3 and the number represented when the digits are interchanged. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! I rewrote both problems slightly.
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The sum of the digits is 8. If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order.
:
Let x = 10's digit of the original number
Let y = units digit of the original number
The number = 10x + y
:
It says the sum of the digits is 8:
x + y = 8
or
y = (8-x); use this for substitution
;
"If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order."
10x + y + 18 = 10y + x
10x - x + 18 = 10y - y
9x + 18 = 9y
Simplify, divide equation by 9
x + 2 = y
Substitute (8-x) for y
x + 2 = 8 - x
x + x = 8 - 2
2x = 6
x =
x = 3
Then y = 5; the original number = 35
:
Check solution in the statement;
"If 18 is added to the number , the digits of the new numeral are those of the original numeral, but they appear in reversed order."
18 + 35 = 53; confirms our solution
:
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The sum of the digits is 8. The number is 16 less than the product of 3 and the number represented when the digits are interchanged.
:
Let x = 10's digit of the original number
Let y = units digit of the original number
The number = 10x + y
:
It says the sum of the digits is 8:
x + y = 8
or
y = (8-x); use this for substitution
;
"The number is 16 less than the product of 3 and the number represented when the digits are interchange"
10x + y = 3(10y+x) - 16
10x + y = 30y + 3x - 16
10x - 3x = 30y - y - 16
7x = 29y - 16
Substitute (8-x) for y:
7x = 29(8-x) - 16
7x = 232 - 29x - 16
7x + 29x = 232 - 16
36x = 216
x =
x = 6
then y = 2; the number = 62
:
Check solution in the statement:
"The number is 16 less than the product of 3 and the number represented when the digits are interchange"
62 = 3(26) - 16
62 = 78 - 16; confirms out solutions
