SOLUTION: The sum of the digits of a three-digit number is 15. The tens digit is 5 more than the units digit. The sum of the hundreds digit and the units digit is 9. Find the number.

Question 95752This question is from textbook
: The sum of the digits of a three-digit number is 15. The tens digit is 5 more than the units digit. The sum of the hundreds digit and the units digit is 9. Find the number. This question is from textbook

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let 100x= the hundreds digit
10y=the tens digit
And z=the units digit
Now we are told that x+y+z=15-------------------eq1
We are also told that:
y=z+1-----------------------------------------------eq2
We are further told that:
x+z=9-----------------------------------------------eq3
In eq3, subtract z from both sides:
x+z-z=9-z collect like terms
x=9-z-----------------------------------------eq3
Next, add eq2 and eq3 and we get:
x+y=10 Now substitute x+y=10 into eq1
10+z=15 subtract 10 from both sides
10-10+z=15-10 collect like terms
z=5-------------------------------units digit
From eq2, y=z+1=5+1=6-----------------------tens digit
From eq3, x=9-z=9-5=4-----------------------------hundreds digit
So our three digit number is: 465
CK
4+6+5=15 ok
15=15
y=z+1
6=5+1 ok
x+z=9
5+4=9
9=9 ok
Hope this helps---ptaylor

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