The numbers 11284 and 7655, when divided by a certain number of three digits, leave the same remainder. find that number of three digits.
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Answered by
67
hey genuis ....
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
I hope that helps.
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
I hope that helps.
Answered by
32
Answer:
Step-by-step explanation:
Total Numbers = 2 (Given)
Number one = 11284 (Given)
Number two = 7655 (Given)
Let the remainder in each case be = x
Thus, then (11284 - x) and (7655 - x) are exactly divisible by that three digit number.
Therefore, the difference will be =(11284−x)−(7655−x)=3629
= 19×191
Three digit no. = 191
Sum of digits of the three digit number = 1 + 9 + 1 = 11
Thus, the required sum of digits of such a three-digit number is 11.
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