Question

Representatives running for office are handing out items to voters. Every 8th voter gets a button. Every 10th voter gets a sticker.

Which voter is the first to receive both items?

Drag and drop the answer into the box to complete the statement.


The th voter receives both items.

a 4th
b 5th
c 8th
d 9th
e 10th
f 24th
g 40th
h 48th
i 80th

Answer 1

i)
Every 8.th voter gets a button:

so a sequence of the voters who receive a button is:

8, 16, 24, 32, ....   that is  8*1, 8*2, 8*3, 8*4, .... in general: 8k for some integer k  

ii)

Every 10.th voter gets a sticker, so the voters who receive stickers are the :

10, 20, 30, 40, .... voters    that is 10*1, 10*2, 10*3, 10*4... in general 10t

for some integer t


iii) what we are looking for is the first number which is 8k and 10t at the same time.

8k=2*2*2k, 
10t=2*5t

Thus this number must be divisible by 2*2*2*5*{some positive integer}

the smallest number is when the positive integer is 1, thus the number is 

2*2*2*5=8*5=40


Answer: g. the 40th