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?

Question

Eliezer Murillo

Mathematics

15 April, 11:05

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?

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Answers (1)

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Isaiah · Answer 1

Nr of chocolates = c

nr of bags of 5 = a

nr of bags of 7 = b

50
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