Question

A number consists of three digits. It remains unchanged if the digits in hundredth and units
place are interchanged. The sum of the three digits is 17 and the difference of the digits in
units and tens place is 4. Find the number.
(Ans. 737)​

Answer 1

Answer:

737, as you already wrote.

Step-by-step explanation:

we want a three digit number, that is a number of the form xyz, where x is the digit in the hundreth place, y is the digit in the tenth place, and z is the digit in the unit place.

We can now write the requirements as equations using x, y, and z:

As the hundredth and unit digits can be interchanged withouth changing the number then $x = z$.

As the sum of the three digits is 17 then $x+y+z = 17$.

As the difference between the units and tens is 4, then $z-y = 4$.

Now we have a system of equations we can solve. We first use the last equation to get an expression for y :  $y = z-4$.

Substituting this into the sum of the digits yields:

$x+y+z = 17 \implies x + (z-4) + z = 17$.

As we also have that $x=z$, then the equation becomes

$z+(z-4)+z=17 \implies 3z - 4 = 17 \implies 3z = 21 \implies z = 7$.

As $x = z$, then $x = 7$.

Substituting the value of z into the expression for y yields

$y = z - 4 = 7 - 4 = 3$.

Hence we have that $x = 7, y = 3, z = 7$, giving us the three digit number

$xyz=737$.

Hope this helps!

Answer 2

Answer:

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Step-by-step explanation:

answers is already given here