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Answer :
To find out how many different combinations of hot dogs and hamburgers Zeke and his friends can buy with exactly [tex]$28.50, let's break down the problem:
1. Understand the Prices:
- Each hot dog costs $[/tex]1.50.
- Each hamburger costs [tex]$3.25.
2. Check the Maximum Purchases:
- First, determine the maximum number of hot dogs that could be bought if only hot dogs were purchased with the entire budget. This would be $[/tex]28.50 divided by [tex]$1.50 per hot dog, which equals 19 hot dogs.
- Next, determine the maximum number of hamburgers that could be bought if only hamburgers were purchased. This would be $[/tex]28.50 divided by [tex]$3.25 per hamburger, which equals 8 hamburgers.
3. Finding Combinations Using a Systematic Approach:
- You need to consider each possible combination of hot dogs and hamburgers that sums up to exactly $[/tex]28.50.
- Start with 0 hot dogs and find out how many hamburgers you can buy to make the total cost [tex]$28.50.
- Increase the number of hot dogs one by one, checking each time how many hamburgers can be added so that the total is still $[/tex]28.50.
- Repeat this process until you reach the maximum possible number of hot dogs (19 hot dogs) and check accordingly with the hamburgers.
4. Count Valid Combinations:
- As you evaluate each scenario, keep track of the combinations where the purchase costs exactly [tex]$28.50.
Through this method, we determine there are 2 valid combinations of hot dogs and hamburgers that exactly total $[/tex]28.50.
With this systematic approach, we arrive at the conclusion that the number of different combinations where you can use the entire budget to buy hot dogs and hamburgers is 2.
1. Understand the Prices:
- Each hot dog costs $[/tex]1.50.
- Each hamburger costs [tex]$3.25.
2. Check the Maximum Purchases:
- First, determine the maximum number of hot dogs that could be bought if only hot dogs were purchased with the entire budget. This would be $[/tex]28.50 divided by [tex]$1.50 per hot dog, which equals 19 hot dogs.
- Next, determine the maximum number of hamburgers that could be bought if only hamburgers were purchased. This would be $[/tex]28.50 divided by [tex]$3.25 per hamburger, which equals 8 hamburgers.
3. Finding Combinations Using a Systematic Approach:
- You need to consider each possible combination of hot dogs and hamburgers that sums up to exactly $[/tex]28.50.
- Start with 0 hot dogs and find out how many hamburgers you can buy to make the total cost [tex]$28.50.
- Increase the number of hot dogs one by one, checking each time how many hamburgers can be added so that the total is still $[/tex]28.50.
- Repeat this process until you reach the maximum possible number of hot dogs (19 hot dogs) and check accordingly with the hamburgers.
4. Count Valid Combinations:
- As you evaluate each scenario, keep track of the combinations where the purchase costs exactly [tex]$28.50.
Through this method, we determine there are 2 valid combinations of hot dogs and hamburgers that exactly total $[/tex]28.50.
With this systematic approach, we arrive at the conclusion that the number of different combinations where you can use the entire budget to buy hot dogs and hamburgers is 2.
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