Question

the number of chocolates Janelle has is more than 50 but less than 70. If she packs them in bags of 5, she would have 2 chocolates left. If she packs them in bags of 7, she would need one more additional chocolate. How many chocolates does Janelle have?

Answer 1

The answer is 62 chocolates.
If you divide 62 into 5 bags, there will be 2 chocolates left. So that's the right answer.
(I couldn't find an easier way, but I had to try numbers from 51 to 69, lol)

Answer 2

nr of chocolates = c
nr of bags of 5 = a
nr of bags of 7 = b

50<c<70

c=5*a+2
c= 7*b-1 therefore b can be max 10 (if b=11 then c=76>70 can't do)
let's say b=10 then c=69 but in this case a=13.4 not integer (also can't do)
let's say b=9 then c=62 then a = 12 wich is ok

solution 1 c=62
let's also try for b=8 wich means c=55 and a=10.6, not integer, not ok again
and also for b=7 wich means c=48 but 48<50 so no go again and also for b<7 wich means c will grow smaller and smaller

so the only solution is c=62