In a 3-digit house number, the hundreds digit is four more than the units digit and the tens digit is twice the units digit. If the sum of the digits is 12, what is the number? Please slove using one variable and explain how to slove the problem.
Thank you
2007-02-24 08:00:58 · 9 answers · asked by abc 1 in Science & Mathematics ➔ Mathematics
The house number is : 624.
Here's how to solve this using simple algebra rather than gussing until "it works." (Although this problem is so simple, that the answer can neither be 400, nor 521, so you hit it next with 642. By the way, for some reason the USPS is adamant about not delivering mail to addresses that have "digits" like 12/7 in them, though this news may disappoint the responder two below me !) :
Let the unit digit be x. Then the tens digit is 2 x, and the hundreds digit is x + 4. These three digits sum to:
x + 2 x + (x + 4) = 4x + 4 = 12 (the given total).
So x = (12 - 4) / 4 = 2, and the house number is:
642.
It's easy to check that this satisfies all the givens.
Live long and prosper.
2007-02-24 08:03:59 · answer #1 · answered by Dr Spock 6 · 0⤊ 0⤋
Writing the 3-digit number as abc, we have
i) a = c + 4,
ii) b = 2c, and
iii) a + b + c=12.
Substituting for a and b from i) and ii) into iii) yields
4c + 4 = 12,
ie. c = 2. Then b =4 and a = 6. Hence the number is 642.
2007-02-24 08:09:37 · answer #2 · answered by MHW 5 · 0⤊ 0⤋
Let x equal the units digit
(4+x)+2x+x=12
collect up the like terms
4+4x = 12
subtract 4 from both sides
4x = 8
Divide by 4
x=2
House number = 642
2007-02-24 08:06:36 · answer #3 · answered by JuJu 3 · 0⤊ 0⤋
the hundreds could not be 1-4
the tens can't be 1, 3, 5, 7, or 9
the ones can't be 9,8,7,6,5,4,3
what of those numbers add up to 12 following those rules?
the ones is 2
the tens is 4
and the hundreds is 6
2007-02-24 08:11:59 · answer #4 · answered by Movie Star 2 · 0⤊ 0⤋
The answer is 642. I used guess and check method. Four more than two is six. If you double two it's four. Add all together and the sum is 12.
2007-02-24 08:06:21 · answer #5 · answered by preetigirl1024 2 · 0⤊ 0⤋
(4 + x) + 2x + x = 12
if x = 2 then
6 + 4 + 2 = 12
the house number is 642
2007-02-24 08:10:07 · answer #6 · answered by srena 5 · 0⤊ 0⤋
assume the unit digit is x and set an expression
(x+4)+2x+x=12
solve it
x+2x+x+4=12
4x+4=12
4x+4-4=12-4
4x=8
4x/4=8/4
x=2
Now put in in order
(x+4)+2x+x=12
(2+4)+2(2)+2=12
6+4+2=12
642
Hope you will get it.
2007-02-24 08:10:52 · answer #7 · answered by Muhammad Faraz Quadri 2 · 0⤊ 0⤋
set up an equation
x = first digit
2x = second digit
4x = third digit
x + 2x + 4x = 12
7x = 12
so x = 12/7
and insert x into the first three equations to find the number
2007-02-24 08:06:28 · answer #8 · answered by sur2124 4 · 0⤊ 1⤋
it is 10 i guess
2007-02-24 08:03:25 · answer #9 · answered by mahassa84 1 · 0⤊ 1⤋