Every 8th person that goes into a store gets a free bottle. every 10th person that goes into a store gets a t-shirt. there are 100 bottles and 100 t shirts to give out. how many people get a t shirt and a bottle

25 persons will get both bottle and t – shirt.

Solution:

Given, every 8th person that goes into a store gets a free bottle.  

And every 10th person that goes into a store gets a t-shirt.  

There are 100 bottles and 100 t shirts to give out.  

We have to find how many people get a t shirt and a bottle

Now, as there are 100 t- shirts, last person to get t – shirt is:

10 x 100 = 1000th person will get last t – shirt

We have to find lcm of 8 and 10, to know who gets both bottle and t – shirt.

So, L.C.M of 8 and 10 = lcm(8, 10)  

= 2 x lcm(4, 5)  

= 2 x 4 x 5 [ as no common factors available for 4 and 5 ]

= 40

So, every 40th person will get both bottle and t – shirt.

Then, out of 1000 people, number of people who get both bottle and t – shirt =

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional