# Prime Factorization Problem 4

## Homework Statement

You bring the drinks for your soccer team every sixth game. Every third game is a home game. How many times will you bring the drinks to a home game if you have a 20 game season?

## Homework Equations

i did the problem in my head, but I need to show my work to get the problem correct. I dont know how i would use factorization to solve this problem

## The Attempt at a Solution

3 games

I think you're right.

Here's how I came up with that.

You've got 20 total games.

Every third game is a home game - that doesn't divide evenly into 20 and since you can't have a half of a game or a third of a game (unless this is some weird version of soccer), then that leaves us with 6 true home games, right? [The closest whole number of 20/3 is 18. 20/3 = 18 2/3 so ~ 18 full games.]

Since you have to bring drinks every six games, then you have to bring drinks 3 times.

Let's draw a chart:

Game # ; Home / Away?; Drinks Y/N?

1; A; N
2; A; N
3; H; N
4; A; N
5; A; N
6; H; Y
7; A; N
8; A; N
9; H; N
10; A; N
11; A; N
12; H; Y
13; A; N
14; A; N
15; H; N
16; A; N
17; A; N
18; H; Y
19; A; N
20; A; N

So yeah, 3 times.

I don't know why I wrote that all out, since I don't have a good explanation as to why it is so...

Blind leading the blind. Good luck!

Hey there,
What learnt from LearningMaths chart is that you bring drinks every 6th game isn't it and every 3rd game is a home game.
.: total no. of home game=20/3=6(We won't consider the decimal part )
so you see,
6 games ,No. of drinks given=1
ie. Every 2 home game ,No. of drinks given=1
.: Every 1 home game ,No. of drinks given=1/2
.: Every 6 home game ,No. of drinks given=1/2*6=3

I think you get my point. But I dont know where the question of prime factorisation rises!!
I wish i could have been of some help!!