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 Phillip could buy so that there are no leftover hot dogs or buns?

Hot dogs 4
Hot dog buns 5

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 4
Hamburger rolls 3

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 or 12,20,15,15

Is that correct? ? If not, can you show me step by step how to get the answer?

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?

The digits 0 through 8 have been classified with the letters A,B and C. How would you classify the digit 9? Why?
A 1 4 7 (9?)
B 2 5
C 0 3 6 8

Is my answer right?

1. To find the smallest number of packages of hot dogs and hot dog buns that Phillip could buy without any leftovers, we need to find the least common multiple (LCM) of 10 and 8.

To do this, we can list the multiples of both numbers and find the smallest one that they have in common:

Multiples of 10: 10, 20, 30, 40, 50...
Multiples of 8: 8, 16, 24, 32, 40...

From the lists, we can see that the smallest common multiple (LCM) of 10 and 8 is 40. Therefore, Phillip could buy 4 packages of hot dogs (4 x 10 = 40) and 5 packages of hot dog buns (5 x 8 = 40) to have no leftovers.

2. Similarly, to find the smallest number of packages of hamburger patties and hamburger rolls without any leftovers, we need to find the LCM of 6 and 8.

Multiples of 6: 6, 12, 18, 24, 30, 36...
Multiples of 8: 8, 16, 24, 32, 40...

The smallest common multiple (LCM) of 6 and 8 is 24. Therefore, Phillip could buy 4 packages of hamburger patties (4 x 6 = 24) and 3 packages of hamburger rolls (3 x 8 = 24) to have no leftovers.

3. To find the smallest number of packages of hot dogs, hamburgers, buns, and rolls that Phillip could buy without any leftovers, we need to consider the LCM of 10, 8, 6, and 8 (since the quantities need to be equal for hot dogs and hamburgers as well).

Multiples of 10: 10, 20, 30, 40, 50...
Multiples of 8: 8, 16, 24, 32, 40...
Multiples of 6: 6, 12, 18, 24, 30, 36...
Multiples of 8: 8, 16, 24, 32, 40...

The smallest common multiple (LCM) of 10, 8, 6, and 8 is 24. Therefore, Phillip could buy 12 packages of hot dogs (12 x 2 = 24), 20 packages of hamburgers (20 x 1 = 20), 15 packages of buns (15 x 2 = 30), and 15 packages of rolls (15 x 2 = 30), to have no leftovers.

4. To calculate the cost of buying hot dogs, hamburgers, buns, and rolls for Phillip's cookout, we need to multiply the number of packages by the cost per package and then add them together.

Hot dogs: 4 packages x $3.29 per package = $13.16
Hamburgers: 20 packages x $3.79 per package = $75.80
Buns: 15 packages x $2.29 per package = $34.35
Rolls: 15 packages x $2.29 per package = $34.35

The total cost would be $13.16 + $75.80 + $34.35 + $34.35 = $157.66.

Regarding the classification of the digit 9, based on the given classification of the digits 0 through 8 as A, B, or C, there is no assigned classification for the digit 9. Therefore, the answer would be None (N/A) or Not classified.

1. To find the smallest number of packages Phillip could buy so that there are no leftover hot dogs or buns, we need to find the least common multiple (LCM) of 10 and 8.

Prime factorize 10: 10 = 2 * 5
Prime factorize 8: 8 = 2^3

The LCM is calculated by taking the highest power of each prime factor that appears in either number. So the LCM of 10 and 8 is: LCM(10, 8) = 2^3 * 5 = 40.

Therefore, the smallest number of packages Phillip could buy is 4 packages of hot dogs (4 * 10 = 40 hot dogs) and 5 packages of hot dog buns (5 * 8 = 40 buns).

2. Similarly, to find the smallest number of packages Phillip could buy so that there are no leftover hamburger patties or rolls, we need to find the LCM of 6 and 8.

Prime factorize 6: 6 = 2 * 3
Prime factorize 8: 8 = 2^3

The LCM is calculated by taking the highest power of each prime factor that appears in either number. So the LCM of 6 and 8 is: LCM(6, 8) = 2^3 * 3 = 24.

Therefore, the smallest number of packages Phillip could buy is 4 packages of hamburger patties (4 * 6 = 24 patties) and 3 packages of hamburger rolls (3 * 8 = 24 rolls).

4. To find the smallest number of packages Phillip could buy so that there are no leftover hot dogs, hamburgers, buns, or rolls, let's find the LCM of 10, 8, 6, and 8.

Prime factorize 10: 10 = 2 * 5
Prime factorize 8: 8 = 2^3
Prime factorize 6: 6 = 2 * 3

The LCM is calculated by taking the highest power of each prime factor that appears in either number. So the LCM of 10, 8, 6, and 8 is: LCM(10, 8, 6, 8) = 2^3 * 3 * 5 = 120.

Therefore, the smallest number of packages Phillip could buy is 12 packages of hot dogs (12 * 10 = 120 hot dogs), 15 packages of hamburger patties (15 * 8 = 120 patties), and 10 packages of both hot dog buns and hamburger rolls (10 * 8 = 80 buns and 10 * 6 = 60 rolls).

To calculate the cost for Phillip to buy hot dogs, hamburgers, buns, and rolls, we need to know the prices per package. Let's assume:

Hot dogs cost $3.29 per package.
Hamburger patties cost $3.79 per package.
Buns and rolls cost $2.29 per package.

The total cost can be calculated by multiplying the number of packages by the price per package and summing the costs:

Cost = (number of hot dog packages * price per hot dog package) + (number of hamburger patty packages * price per hamburger patty package) + (number of bun packages * price per bun package) + (number of roll packages * price per roll package)

Let's say Phillip buys 12 packages of hot dogs, 15 packages of hamburger patties, 10 packages of hot dog buns, and 10 packages of hamburger rolls. Substituting the values:

Cost = (12 * $3.29) + (15 * $3.79) + (10 * $2.29) + (10 * $2.29) = $39.48 + $56.85 + $22.90 + $22.90 = $142.13

Therefore, it will cost Phillip $142.13 to buy hot dogs, hamburgers, buns, and rolls for his cookout.

About classifying the digits:
Based on the given classification, the digit 9 would fall under category C because it is grouped with 0, 3, 6, and 8.

1 and 2 are correct.

4. If there are equal numbers of hamburgers and hot dogs, you have to have 3 packages of hot dogs for every 5 packages of hamburgers. If they are 12 and 20, respectively, then the buns are 15 and 15, respectively.

Are you sure you don't have a typo for the last question? If each number increased by 3, then the below would apply.

A 1 4 7
B 2 5 8
c 0 3 6 (9)