Jack has 99 hot dogs and 261 hot dog buns. He wants to put the same number of hot dogs and hot dog buns on each tray. What is the greatest number of trays Jack can use to accomplish this?
Ok you know that there are only going to be able to be 99 hot dogs and 99 hot dog buns in order to make the problem work.
99 + 99 = 198
Then take 198 and divide by even numbers because you know that you will have to have 1 hot dog and 1 bun (2 together) to see how much is the most you will be able to put onto the trays.
He can use 99 trays and have 1 hot dog and 1 hot dog bun.
Thank you for walking me through the problem. You are greatly appreciated:)
Well, Jack seems to be in a pickle with his hot dogs and hot dog buns. It's quite a "bunderful" situation. Let's do a little math and solve it together, shall we?
To find the greatest number of trays Jack can use, we need to figure out the common factor between 99 and 261. So, let's grab our funny math hats and get to work!
The prime factorization of 99 is 3 * 3 * 11, while the prime factorization of 261 is 3 * 3 * 29.
To make the common factors match, we can have 3 * 3 = 9 hot dogs and 3 * 29 = 87 hot dog buns on each tray. By dividing the total number of hot dogs (99) by 9, we find that Jack can use 11 trays. So, the greatest number of trays is 11!
Voila! Jack can have a "tray-mendous" hot dog party with 11 trays. Just imagine the clown-doggery that'll go on with that many hot dogs and buns!
To find the greatest number of trays that Jack can use to accommodate the same number of hot dogs and hot dog buns, we need to determine the common factor of 99 and 261. This common factor will represent the number of hot dogs and hot dog buns that can be evenly divided.
To find the common factor, we can use prime factorization.
Prime factorization of 99:
99 = 3 * 3 * 11
Prime factorization of 261:
261 = 3 * 3 * 29
Now, we can find the common factors by identifying the shared prime factors:
Common factors: 3 * 3 = 9
Therefore, the greatest number of trays that Jack can use to accomplish having the same number of hot dogs and hot dog buns is 9.