OIL 10The sum of the digits of a three-digit number is 11. If the digi

1.	OIL 10The sum of the digits of a three-digit number is 11. If the digits are reversed, the newnumber is 46 more than five times the former number. If the hundreds digit plus twicethe tens digit is equal to the units digit, then find the original three digit number?
Answer» Let the number be: 100x + 10y + z Let's try solving this using only the 1st and last statements:"The sum of the digits of a three-digit number is 11."x + y + z = 11 "the hundreds digit plus twice the tens digit is equal to the units digit,"x + 2y = zx + 2y - z = 0 Add to the 1st equation to eliminate zx + y + z = 11x +2y - z = 0--------------2x + 3y = 11 2x = 11 - 3y x =(11 - 3y)/2 Only two values for y will give a positive integer value for x, namely 1 and 3. From the 2nd statement we know that x is a low value, therefore 3 seems likely:x =(11 - 3*3)/2x = (11 - 9)/2x = 2/2x = 1 when y = 3 Find z1 + 3 + z = 11z = 11-4z = 7 Our number is 137

OIL 10The sum of the digits of a three-digit number is 11. If the digits are reversed, the newnumber is 46 more than five times the former number. If the hundreds digit plus twicethe tens digit is equal to the units digit, then find the original three digit number?

Answer»

Let the number be: 100x + 10y + z

Let's try solving this using only the 1st and last statements:"The sum of the digits of a three-digit number is 11."x + y + z = 11

"the hundreds digit plus twice the tens digit is equal to the units digit,"x + 2y = zx + 2y - z = 0

Add to the 1st equation to eliminate zx + y + z = 11x +2y - z = 0--------------2x + 3y = 11

2x = 11 - 3y

x =(11 - 3y)/2

Only two values for y will give a positive integer value for x, namely 1 and 3.

From the 2nd statement we know that x is a low value, therefore 3 seems likely:x =(11 - 3*3)/2x = (11 - 9)/2x = 2/2x = 1 when y = 3

Find z1 + 3 + z = 11z = 11-4z = 7

Our number is 137