Tina and Bruce are each rolling a 1 to 6 number cube. They are looking for different ways to roll two factors whose product is greater than 14. How many different ways will they find? Product means to multiply so 4x5, 3x5,6x5,. I chose 1 to 6 SO I have three times.
Apparently answer is 13 or 8. Got it wrong first time and this is answers I got corrected with.
Oh, I see! Tina and Bruce are on a mission to find pairs of numbers on their number cubes that, when multiplied, give them a product greater than 14. Let's see how many different ways they can achieve this comedic math feat!
First, Tina rolls the dice and gets a 4. She can team up with any number on the other dice to make a product greater than 14. So, she can choose from 5 and 6. That gives her two options: 4 x 5 and 4 x 6.
Next up is Bruce, and he rolls a 3. Similar to Tina, he needs to pair up with numbers that will give him a product greater than 14. He can choose from 5 and 6, just like Tina. So, he also has two options: 3 x 5 and 3 x 6.
Adding up Tina's and Bruce's possibilities, we get a total of 4 different ways they can roll two factors whose product is greater than 14.
To summarize:
- Tina can roll 4 x 5 or 4 x 6, giving her two options.
- Bruce can roll 3 x 5 or 3 x 6, also giving him two options.
- Hence, they have a grand total of 4 different ways to achieve their math quest.
Now, go forth, Tina and Bruce, and may your dice roll in your favor!
To find the different ways Tina and Bruce can roll two factors whose product is greater than 14 using a standard six-sided die, we need to consider all possible pairs of numbers that satisfy this condition.
Let's break it down step by step:
Step 1: List all the possible outcomes for each person's roll of the die.
- Tina's possible outcomes: 1, 2, 3, 4, 5, 6
- Bruce's possible outcomes: 1, 2, 3, 4, 5, 6
Step 2: Determine the factors for each pair.
- Tina rolls: 1
- There is no pair with a product greater than 14.
- Tina rolls: 2
- There is no pair with a product greater than 14.
- Tina rolls: 3
- Bruce rolls: 5 (3 x 5 = 15)
- Possible pair: (3, 5)
- Tina rolls: 4
- Bruce rolls: 5 (4 x 5 = 20)
- Bruce rolls: 6 (4 x 6 = 24)
- Possible pairs: (4, 5), (4, 6)
- Tina rolls: 5
- Bruce rolls: 3 (5 x 3 = 15)
- Bruce rolls: 4 (5 x 4 = 20)
- Bruce rolls: 5 (5 x 5 = 25)
- Bruce rolls: 6 (5 x 6 = 30)
- Possible pairs: (5, 3), (5, 4), (5, 5), (5, 6)
- Tina rolls: 6
- Bruce rolls: 4 (6 x 4 = 24)
- Bruce rolls: 5 (6 x 5 = 30)
- Bruce rolls: 6 (6 x 6 = 36)
- Possible pairs: (6, 4), (6, 5), (6, 6)
Step 3: Count the number of different ways they find.
- Total number of ways: 1 + 2 + 4 = 7
Therefore, Tina and Bruce can find different ways to roll two factors whose product is greater than 14 in a total of 7 different ways.
To determine the number of different ways Tina and Bruce can roll two factors whose product is greater than 14 using a 1 to 6 number cube, we can follow these steps:
1. Identify the prime factors of numbers greater than 14 within the given range (1 to 6).
- 15: Prime factors = 3, 5
- 16: Prime factors = 2
- 18: Prime factors = 2, 3
- 20: Prime factors = 2, 5
- 24: Prime factors = 2, 3
- 25: Prime factors = 5
- 30: Prime factors = 2, 3, 5, 7
- 36: Prime factors = 2, 3
2. List out all the possible combinations of these prime factors taking two at a time.
- 3 * 5 = 15
- 2 * 2 = 4
- 2 * 3 = 6
- 2 * 5 = 10
- 2 * 3 = 12
- 5 * 5 = 25
3. Check which of these combinations fall within the given range of 1 to 6.
- 10, 12, and 25 fall within the range.
Therefore, Tina and Bruce will find three different ways to roll two factors whose product is greater than 14: 10, 12, and 25.
3x6
3x5
4x4
4x5
4x6
(5x3) -- already have it
(5x4)
5x6
(6x3)
(6x4)
(6x5)
6x6
I see 7 of them