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 =

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for