I. For the following exercises, use this scenario: Kelly opened a bag of colored chocolate coated candies and counted the number of each color of candy. She found she had 9 green, 4 yellow, 13 black, 11 orange, 8 blue, and 7 red. What is the ratio of the following candy colors?
1. Red candies to green candies
2. Green candies to black candies
3. Yellow candies to black candies
4. Black candies to blue candies
5. Orange candies to non-orange candies
6. Yellow candies to non-yellow candies
7. Red candies to all candies
8. Pink candies to all candies
1. The ratio of red candies to green candies is 7:9.
2. The ratio of green candies to black candies is 9:13.
3. The ratio of yellow candies to black candies is 4:13.
4. The ratio of black candies to blue candies is 13:8.
5. The ratio of orange candies to non-orange candies is 11:(9+4+13+8+7).
6. The ratio of yellow candies to non-yellow candies is 4:(9+13+11+8+7).
7. The ratio of red candies to all candies is 7:(9+4+13+11+8+7).
8. The ratio of pink candies to all candies is 0: (since there are no pink candies mentioned in the scenario).
To find the ratio of candy colors, we need to compare the number of candies of one color to the number of candies of another color or to the total number of candies.
1. Red candies to green candies:
- Number of red candies = 7
- Number of green candies = 9
- Ratio of red candies to green candies = 7:9
2. Green candies to black candies:
- Number of green candies = 9
- Number of black candies = 13
- Ratio of green candies to black candies = 9:13
3. Yellow candies to black candies:
- Number of yellow candies = 4
- Number of black candies = 13
- Ratio of yellow candies to black candies = 4:13
4. Black candies to blue candies:
- Number of black candies = 13
- Number of blue candies = 8
- Ratio of black candies to blue candies = 13:8
5. Orange candies to non-orange candies:
- Number of orange candies = 11
- Number of non-orange candies = sum of all other colored candies = 9 + 4 + 13 + 8 + 7 = 41
- Ratio of orange candies to non-orange candies = 11:41
6. Yellow candies to non-yellow candies:
- Number of yellow candies = 4
- Number of non-yellow candies = sum of all other colored candies = 9 + 13 + 11 + 8 + 7 = 48
- Ratio of yellow candies to non-yellow candies = 4:48
7. Red candies to all candies:
- Number of red candies = 7
- Total number of candies = sum of all colored candies = 9 + 4 + 13 + 11 + 8 + 7 = 52
- Ratio of red candies to all candies = 7:52
8. Pink candies to all candies:
- Number of pink candies = 0 (based on the given scenario)
- Total number of candies = sum of all colored candies = 9 + 4 + 13 + 11 + 8 + 7 = 52
- Ratio of pink candies to all candies = 0:52
To find the ratio of different candy colors, we need to compare the numbers of each color. Here's how you can calculate each ratio:
1. Red candies to green candies:
Divide the number of red candies (7) by the number of green candies (9):
Ratio = 7/9 = 0.7777 (rounded to four decimal places)
Therefore, the ratio of red candies to green candies is approximately 0.7777.
2. Green candies to black candies:
Divide the number of green candies (9) by the number of black candies (13):
Ratio = 9/13 = 0.6923 (rounded to four decimal places)
Therefore, the ratio of green candies to black candies is approximately 0.6923.
3. Yellow candies to black candies:
Divide the number of yellow candies (4) by the number of black candies (13):
Ratio = 4/13 = 0.3077 (rounded to four decimal places)
Therefore, the ratio of yellow candies to black candies is approximately 0.3077.
4. Black candies to blue candies:
Divide the number of black candies (13) by the number of blue candies (8):
Ratio = 13/8 = 1.625 (rounded to three decimal places)
Therefore, the ratio of black candies to blue candies is approximately 1.625.
5. Orange candies to non-orange candies:
Add up the numbers of all non-orange candies (green, yellow, black, blue), which totals 9 + 4 + 13 + 8 = 34.
Divide the number of orange candies (11) by the number of non-orange candies (34):
Ratio = 11/34 = 0.3235 (rounded to four decimal places)
Therefore, the ratio of orange candies to non-orange candies is approximately 0.3235.
6. Yellow candies to non-yellow candies:
Add up the numbers of all non-yellow candies (green, black, orange, blue), which totals 9 + 13 + 11 + 8 = 41.
Divide the number of yellow candies (4) by the number of non-yellow candies (41):
Ratio = 4/41 = 0.0976 (rounded to four decimal places)
Therefore, the ratio of yellow candies to non-yellow candies is approximately 0.0976.
7. Red candies to all candies:
Add up the numbers of candies of all colors, which totals 9 + 4 + 13 + 11 + 8 + 7 = 52.
Divide the number of red candies (7) by the number of all candies (52):
Ratio = 7/52 = 0.1346 (rounded to four decimal places)
Therefore, the ratio of red candies to all candies is approximately 0.1346.
8. Pink candies to all candies:
There is no information given regarding pink candies, so the ratio cannot be calculated.