Answer :
Sure, let's break down the solutions for each part of the question step by step.
### Part 1: Red and Blue Smarties
We need to find out how many red Smarties are in the box if the total number of Smarties is 24 and the ratio of blue to red Smarties is 1:3.
1. Understand the Ratio:
- Blue : Red = 1 : 3
- This means for every 1 blue Smartie, there are 3 red Smarties.
2. Total Parts in Ratio:
- Add the parts of the ratio together: [tex]\(1 (blue) + 3 (red) = 4\)[/tex] parts.
3. Calculate the Value of Each Part:
- If 4 parts correspond to 24 Smarties, then each part represents [tex]\(\frac{24}{4} = 6\)[/tex] Smarties.
4. Calculate Number of Red Smarties:
- Red Smarties make up 3 parts of the ratio.
- Therefore, the number of red Smarties is [tex]\(3 \times 6 = 18\)[/tex].
So, there are 18 red Smarties in the box.
### Part 2: Dividing Sweets Between Johan and Anthony
We need to divide 36 sweets between Johan and Anthony in the ratio 3:4.
1. Understand the Ratio:
- Johan : Anthony = 3 : 4
2. Total Parts in Ratio:
- Add the parts of the ratio together: [tex]\(3 (Johan) + 4 (Anthony) = 7\)[/tex] parts.
3. Calculate the Value of Each Part:
- If 7 parts correspond to 36 sweets, then each part represents [tex]\(\frac{36}{7}\)[/tex].
4. Calculate Number of Sweets Johan Gets:
- Johan gets 3 parts.
- Johan's sweets = [tex]\(3 \times \frac{36}{7} \approx 15.43\)[/tex]
5. Calculate Number of Sweets Anthony Gets:
- Anthony gets 4 parts.
- Anthony's sweets = [tex]\(4 \times \frac{36}{7} \approx 20.57\)[/tex]
Thus, Johan gets approximately 15.43 sweets, and Anthony gets approximately 20.57 sweets. However, because you can't have a fraction of a sweet, you'd need to decide based on the context how to practically distribute any remaining sweets.
### Part 1: Red and Blue Smarties
We need to find out how many red Smarties are in the box if the total number of Smarties is 24 and the ratio of blue to red Smarties is 1:3.
1. Understand the Ratio:
- Blue : Red = 1 : 3
- This means for every 1 blue Smartie, there are 3 red Smarties.
2. Total Parts in Ratio:
- Add the parts of the ratio together: [tex]\(1 (blue) + 3 (red) = 4\)[/tex] parts.
3. Calculate the Value of Each Part:
- If 4 parts correspond to 24 Smarties, then each part represents [tex]\(\frac{24}{4} = 6\)[/tex] Smarties.
4. Calculate Number of Red Smarties:
- Red Smarties make up 3 parts of the ratio.
- Therefore, the number of red Smarties is [tex]\(3 \times 6 = 18\)[/tex].
So, there are 18 red Smarties in the box.
### Part 2: Dividing Sweets Between Johan and Anthony
We need to divide 36 sweets between Johan and Anthony in the ratio 3:4.
1. Understand the Ratio:
- Johan : Anthony = 3 : 4
2. Total Parts in Ratio:
- Add the parts of the ratio together: [tex]\(3 (Johan) + 4 (Anthony) = 7\)[/tex] parts.
3. Calculate the Value of Each Part:
- If 7 parts correspond to 36 sweets, then each part represents [tex]\(\frac{36}{7}\)[/tex].
4. Calculate Number of Sweets Johan Gets:
- Johan gets 3 parts.
- Johan's sweets = [tex]\(3 \times \frac{36}{7} \approx 15.43\)[/tex]
5. Calculate Number of Sweets Anthony Gets:
- Anthony gets 4 parts.
- Anthony's sweets = [tex]\(4 \times \frac{36}{7} \approx 20.57\)[/tex]
Thus, Johan gets approximately 15.43 sweets, and Anthony gets approximately 20.57 sweets. However, because you can't have a fraction of a sweet, you'd need to decide based on the context how to practically distribute any remaining sweets.
