Jonah has a large collection of marbles he notices that if he borrows five marbles from a from a friend he can arrange the marbles in rows of 13 inch what is the remainder when he divides original number of marbles by 13

The remainder is 8

Step-by-step explanation:

Let Jonah's Marble=x

If he arranges x marbles into y rows of 13 each, and there are remainders (R)

Then:

x/13=y + (R/13) ... (I)

If he borrows 5 marbles from a friend, there will be no remainder. However, the number of rows y, will be increased by 1

New Total Marbles=x+5

(x+5) / 13=y+1 ... (ii)

x+5=13 (y+1)

x=13y+13-5

x=13y+8

From (I)

x=13y+R

Comparing the values of x derived from (I) and (ii)

13y+R=13y+8

Therefore the Remainder, R = 8