Question 551146: The value of a certain two digit number is 4 more than six times the sum of it's digits. If the digits are reversed, the resulting number is 18 less than the original number. What is the original number? Please hel
Found 2 solutions by mathstutor458, lwsshak3:
Answer by mathstutor458(57)   (Show Source):
You can put this solution on YOUR website! let the number is xy
The value of a certain two digit number is 4 more than six times the sum of it's digits.
so,xy=6(x+y)+4
If the digits are reversed, the resulting number is 18 less than the original number.
which means, yx=xy-18=6(x+y)+4-18=6(x+y)-14
here x,y values must be even numbers to satisfies the equation.
let us take the numbers randomly
let x=4,y=2,so xy=42 (in this problem x value must be greater because,yx=xy-18)
yx=6(x+y)-14 = 6(4+2)-14 = 36-14=22 doesnot satisfies the condition
let x=6,y=2,so xy=62
yx=6(x+y)-14 = 6(6+2)-14 = 48-14=34 doesnot satisfies the condition
let x=6,y=4,so xy=64
yx=6(x+y)-14 = 6(6+4)-14 =60-14=46
46=46 satisfies the equation
so,original number is 64.
Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! The value of a certain two digit number is 4 more than six times the sum of it's digits. If the digits are reversed, the resulting number is 18 less than the original number. What is the original number?
**
let t=ten's digit
let u=unit's digit
original 2-digit number=10t+u
10t+u=6(t+u)+4 (two digit number is 4 more than six times the sum of it's digits)
10t+u=6t+6u+4
10t+u=10u+t+18 (digits are reversed, the resulting number is 18 less than the original number)
..
4t-5u=4
9t-9u=18
..
36t-45u=36
36t-36u=72
-9u=-36
u=4
4t-5u=4
4t=24
t=6
original number=64
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