. Two numbers 11284 and 7655, when divided by a certain number of three digits, leaves the same remainder. The sum of digits of such a three-digit number is
Answers
Answer:
.
You Have to find a three-digit Number X such that 11284 / X and 7655 / X Leave the same remainder R. In other words:
(equation 1) mX + R = 11284
(equation 2) nX + R = 7655
Where M and n are Whole number Multiples. We want to Combine the Equations, so we'll Make Equation 2 Negative throuhout. That'll Eliminate the Remainder so we can Focus more on X.
(equation 2.1) -nX - R = -7655
Now we Combine the equations to get:
(equation 3) (m - n)X = 11284 - 7655
(equation 3.1) (m - n)X = 3629
m and N are whole Numbers, and Since mX + R is Greater than nX + R, it Follows that m is larger than n; therefore, m - n is also a whole Number. Let's call it z.
(equation 4) zX = 3629
To Find X, we Have to be Able to find three-digit factors of 3629. start by Finding the Smallest Prime number that will Divide evenly into 3629. 2 won't, 3 Won't, 5 won't, 7 won't, 11 won't, 13 won't, 17 won't, but 19 will. 19 x 191 = 3629. And as it turns out, that makes X a three-digit Number, so it satisfies your Requirements and we can stop Searching.
To check, Divide 11284 and 7655 by 191 to confirm that they Give the same remainder:
11284 / 191 = 59 R15
7655 / 191 = 40 R15
#answerwithquality #bal