How many times will you bring drinks to a home game in a 20 game season?

[shawonna23]

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 don't know how i would use factorization to solve this problem

The Attempt at a Solution

3 games

 

[LearningMath]

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!

 

[1/2"]

Hey there,
What learned 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 don't know where the question of prime factorisation rises!
I wish i could have been of some help!