SOLUTION: Sarah has a collection of marbles. She notices that if she borrows 8 marbles from a friend, then she can arrange the marbles in rows of 15 each. What is the remainder when she divi

Question 380322: Sarah has a collection of marbles. She notices that if she borrows 8 marbles from a friend, then she can arrange the marbles in rows of 15 each. What is the remainder when she divides her original number of marbles by 15?

Found 2 solutions by stanbon, richard1234:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Sarah has a collection of marbles. She notices that if she borrows 8 marbles from a friend, then she can arrange the marbles in rows of 15 each. What is the remainder when she divides her original number of marbles by 15?
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Let original number of marbles be "x":
x+8 = 15k where k is the number of rows.
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x = 15k-8
x = [15(k-1) + 15]-8
x = [15(k-1)]+7
x/15 = (15(k-1)+7)/15
x/15 = (k-1)+(7/15)
---
Quotient = (k-1)
Remainder = 7
====================
Cheers,
Stan H.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Using basic modular arithmetic, if x + 8 is a multiple of 15, then x + 8 = 0(modulo 15). Subtracting 8 from both sides, we get x = -8 = 7 (modulo 15). The remainder is therefore, 7.
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