A store owner can exchange 9 used batteries for 1 new battery. If he has 961 used batteries, how many new can he obtain?

[Johnny V]

A store owner can exchange 9 used batteries for 1 new battery . If he has 961 used batteries , how many new can he obtain ? The answer is 120 .
I hoped that dividing 961 / 9 would yield the answer . When you divide the above it comes to 106 . Should I continue & divide 106 by 9 , 11 by 9 , & add the remainders to 106 ? Thank you .

 

[stapel]

A store owner can exchange 9 used batteries for 1 new battery . If he has 961 used batteries , how many new can he obtain ? The answer is 120 .
I hoped that dividing 961 / 9 would yield the answer . When you divide the above it comes to 106 . Should I continue & divide 106 by 9 , 11 by 9 , & add the remainders to 106 ? Thank you .

My guess is that there is an error in the answers in the back of the book, unless....

If they are asking how many batteries he could get from the original set, and then also from what he got in trade, then you would want to continue counting.

However, don't forget the leftovers. The first batch of dead batteries contained 961 batteries, of which he could exchange 106. But this leaves him with 7 dead batteries. Now assume that he drains the 106 batteries. At this point, he has 106+7 = 113 dead batteries. How many can he trade in? How many are left over?

Continue until you get their answer (based on the unstated assumption that he's repeatedly trading).

Eliz.

 

[The Highlander]

A store owner can exchange 9 used batteries for 1 new battery . If he has 961 used batteries , how many new can he obtain ? The answer is 120 .
I hoped that dividing 961 / 9 would yield the answer . When you divide the above it comes to 106 . Should I continue & divide 106 by 9 , 11 by 9 , & add the remainders to 106 ? Thank you .

Yes, if you want to get the same answer as the back of the book. ?

But you don't divide "106 by 9" or "11 by 9"!

The store owner starts with 961 UBs (used batteries).
Dividing that by 9 means he can get 106 NBs (new batteries).
To do that he exchanged 954 UBs for 106 NBs but that left him with 7 UBs still in his possession.

So when the 106 NBs are "used" he will then have (106+7) 113 UBs that he can now exchange for NBs.
That means he can get 113÷9=12 NBs with 5 UBs left over. (So it is 113 you need to divide by 9 not 106!)

So it is 17 (12+5) that you need to divide by 9 at this (next) stage (not 11!).

So, by now, he has been able exchange UBs for NBs to get a total of (106+12) 118 NBs, in total, so far.

If you continue this 'process' (correctly) you should be able to demonstrate that he does, indeed, end up being able to "obtain" (in total) 120 NBs and be left (eventually) with only a single battery at the end.