What Number has 3 ten thousands, 1 more thousand than ten thousands, 3 more hundreds than thousands, 3 fewer tens than hundreds, and 3 more ones than tens?

Question

What Number has 3 ten thousands, 1 more thousand than ten thousands, 3 more hundreds than thousands, 3 fewer tens than hundreds, and 3 more ones than tens?

Answer 1

Let the number of ten thousands = a

Let the number of thousands = b

Let the number of hundreds = c

Let the number of tens = x

Let the number of ones = y

 

 

Now that we set our variables, we can set equations based on the description.

 

a = 3                    eq1

b - a = 1                eq2

c - b = 3                eq3

c - x = 3               eq4

y - x = 3               eq5

 

 

We have 5 equations with 5 variables.   Since we know the value of one of the variables, we can substitute it into the next equation.  Then use the result to substitute into the equation after that and so on.

 

b - 3 = 1                      eq2

b = 4

 

c - 4 = 3                      eq3

c = 7

 

7 - x = 3                      eq4

    x = 4

 

y - 4 = 3                      eq5

y = 7

 

 

These values that we solved for are the digits of the number.  This number will have 5 digits.  The first digit is a,  and the last digit is y, knowing your place values.

 

The number is   34747