Leah and Sam were playing a game with two dice. They took turns rolling the dice and finding the products of the numbers rolled. To make the game fair, if Leah rolls a certain product she gets 2 points. If Sam rolls a certain product, he gets 3 points. What might the products be?
Leah rolled 1 and 1
Sam rolled 1 and 2
xx 1 2 3 4 5 6
-------------
1| 1 2 3 4 5 6
2| 2 4 6 8 10 12
3| 3 6 9 12 15 18
4| 4 8 12 16 20 24
5| 5 10 15 20 25 30
6| 6 12 18 24 30 36
well Leah's number must happen 3 times for every 2 of Sam's
for example
2 happens twice (Sam)
4 happens 3 times (Leah)
is there a four times and a six times?
To determine the possible products on the dice, let's find the product of Leah and Sam's rolls and check if it matches any of the possible products.
Leah rolled a 1 and 1, so the product would be 1 * 1 = 1.
Sam rolled a 1 and 2, so the product would be 1 * 2 = 2.
Now we need to find the products where Leah gets 2 points and Sam gets 3 points. To do this, we divide the product by 1 point for Leah (2/1 = 2) and by 3 points for Sam (2/3 ≈ 0.67). We then find the closest whole number to the result.
For Leah to get 2 points, the possible products are:
1 * 1 = 1 (which matches her roll)
For Sam to get 3 points, the possible products are:
1 * 2 = 2 (which matches his roll)
So, the products that would give Leah 2 points and Sam 3 points in this game are 1 and 2, respectively.