Question

my thousand digit is 2 more than my tens digit my hundred digit is 3 more than my tens digit and my ones digit is 2 less than my hundred digit if my ten digit is 5 what number am i

Answer 1

Answer:

Let’s set each digit equal to a variable:

x = thousands digit

y = hundreds digit

z = tens digit

a = ones digit

From the statement in your question we are given the following equations:

x = 2a

y = a+2

z = x-y

Since z = x-y, the following statement is true:

z = 2a-(a+2)

z = 2a-a-2

z = a-2

So x = 2a, y = a+2, and z = a-2. The only variable we don’t have a value for is a. If we find that we can find the value of each other variable.

There is a critical restriction on what each variable can be: since we are using the base-10 numbering system that means there are only 10 possible values for each variable. X cannot be equal to zero because that means we would have a 3-digit number when the question says we have a 4-digit number.

since x = 2a, a would have to be either 4, 3, 2, or 1 as this would make x equal to 8, 6, 4, or 2, respectively, and fulfill the restriction. There is another restriction, too, and that is for z:

z = a-2

the result of that equation is that z could be equal to 0, which would make a equal to 2, but a cannot be equal to 1 because that would make z negative.

This narrows down the possible values for a to just 2, 3, or 4

So let’s try this with a = 2:

x = 2a

x = 2*2

x = 4

y = a+2

y = 4

z = a-2

z = 2–2

z = 0

So if a = 2, then x = 4, y = 4, and z = 0

The number would be 4,402

Do the other possible values work…? Let’s try a = 3

a = 3

x = 2a

x = 2*3

x = 6

y = a+2

y = 3+2

y = 5

z = a-2

z = 3–2

z = 1

Answer 2

Answer:

The required number = 7856

Step-by-step explanation:

Let x,y,z,w be the thousands, hundreds, tens and one's digit respectively

By the given conditions

The thousand's digit is 2 more than the tens digit,  we have

x = 2+z ----------------(1)

The hundred digit is 3 more than tens digit

y = 3 +z ---------------(2)

Ones digit is 2 less than hundred digit

w = y -2 ---------------(3)

Ten's digit of the number = z = 5

From equation (1) we have

Thousand's digit  x = 2 + z = 7

From equation (2) we have

Hundred's digit =y =  3 +z = 3+5 = 8

From equation (3)

ones digit =  w = y -2 = 8 -2 = 6

∴ x = 7 , y = 8 , z = 5 , w = 6

∴ The required number = 7856

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