Are my answers right please?
1. Hot dogs come 10 to a package, and hot dog buns come 8 to a package. What is the smallest number of packages of each that Ms. Evans could buy so that there are no leftover hot dogs or buns?
Hot dogs 4 packages
Hot dog buns 5 packages
2. Hamburger patties come 6 to a package, and hamburger rolls come 8 to a package. What is the smallest number of packages of each that Phillip could buy so that there are no leftover hambergers or rolls?
Hamburger patties 4packages
Hamburger rolls 3packages
4.Phillip is having a cookout. Phillip wants to buy an equal number of hot dogs and hamburgers. What is the smallest number of packages of each that Phillip could buy so that there are no leftover hot dogs, hamburgers, buns, or rolls?
12,20,24,40
4.Hot dogs cost $3.29 per package, hamburger patties cost $3.79 perpackage, and buns and rolls cost $2.29 per package. What will it cost Phillip to buy hot dogs, hamburgers, buns, and rolls for his cookout?
$261.84
At the first meeting of Manchester backgammon club the members decided to have a tournament to determine who their best players were. Each member played one game with every other member. How many games were played altogether if there are ten members in the club???
I agree with your answers to the first 4 questions.
for the last:
Each of the 10 players plays against the other 9.
So that is 90
But...
it includes A vs B and B vs A, which is the same game, so we divide the above by 2
so there are 45 games.
Or ... short-cut way
choose pairs of 2's from 10
= C(10,2) = 45
To determine the number of games played in the backgammon tournament, you can use a combination formula. In this case, each member plays one game with every other member, so for each member, there will be 9 games played (excluding themselves).
Since there are 10 members in the club, you can calculate the total number of games played by multiplying the number of games each member plays (9) by the number of members (10).
Number of games played = (Number of members) x (Number of games each member plays)
= 10 x 9
= 90
Therefore, there were 90 games played altogether in the backgammon tournament.