Question 208260: You have a four digit number where the thousands digit is four greater than the hundreds digit. The tens digit is twice the thousands digit. The ones digit is half of the thousands digit. What is the number?
How would you set up this type of problem and what is the equation for it.
Found 2 solutions by jsmallt9, ankor@dixie-net.com:
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! This one is probably easier to solve with logic than with Algebra.
First let's consider the digits of a 4-digit number. The first digit, the thousands digit, may be any digit except zero. If the first digit was zero, we would only have a 3-digit number. The other digits may be any of the ten digits.
Now let's look at the facts.- You have a four digit number where the thousands digit is four greater than the hundreds digit. This tells us
- that the thousands digit must be greater than or equal to 4 (since the hundreds digit cannot be lower than 0).
- that the hundreds digit must be less than 6 (or else the thousands digit would be more than 10).
- The tens digit is twice the thousands digit. This tells us
- that the tens digit must be even
- that the thousands digit must be less than or equal to 4 (or else the tens digit would be greater than or equal to 10)
- The ones digit is half of the thousands digit. This tells us that the thousands digit is even (or else the ones digit, which is 1/2, would not be a whole number).
So the first fact tells us that the thousands digit must be greater than or equal to 4. The second fact tells us that the thousands digit must be less than or equal to 4. The only number that is greater than or equal to 4 and less than or equal to 4 at the same time is 4! So the thousands digit must be 4.
Since the thousands digit is 4 more than the hundreds digit and since the thousands digit is 4, the hundreds digit must be 0.
Since the tens digit is twice the thousands digit and since the thousands digit is 4, the tens digit must be 8.
Since the ones digit is half the thousands digit and since the thousands digit is 4, the tens digit must be 2.
So the number is 4082.
This could be done with a bunch of inequalities and equations (i.e. Algebra) but it is easier this way.
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! You have a four digit number where the thousands digit is four greater than the hundreds digit.
The tens digit is twice the thousands digit.
The ones digit is half of the thousands digit.
What is the number?
:
The 4 digit number: 1000a + 100b + 10c + d
:
"the thousands digit is four greater than the hundreds digit."
a = b + 4
or
b = a - 4 means a => 4
:
" The tens digit is twice the thousands digit." means a < 5
c = 2a
:
" The ones digit is half of the thousands digit." means a is an even number
d = .5a
:
What is the number?
:
From the given information we conclude that a = 4, b = 0, c = 8, d = 2
:
Our number: 4082
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