A food packing company makes a popular

Question

fruit cocktail. To ensure a good mixture of fruit,
there are 3 cherry halves for every 8 white
grapes in a jar. An inspector notices that one jar
has 12 cherry halves and 20 white grapes. What
can be done to fix the error?

Answer 1

To fix the error and ensure a good mixture of fruit in the jar, the following steps can be taken:

1. Determine the ratio between the cherry halves and white grapes:
- The current ratio is 3 cherry halves: 8 white grapes.
- Simplifying the ratio by dividing both numbers by their greatest common divisor (GCD), the ratio becomes 3:8.

2. Calculate the total number of cherry halves and white grapes in the jar:
- The jar currently contains 12 cherry halves and 20 white grapes.

3. Determine the number of sets of the ratio that can fit in the jar:
- Dividing the number of cherry halves (12) by 3, we find that there are 4 sets of the ratio in the jar.
- Dividing the number of white grapes (20) by 8, we find that there are 2 sets of the ratio in the jar.

4. Compare the number of sets of the ratio:
- Since there are fewer sets of the ratio for white grapes (2) compared to cherry halves (4), the error lies in the portion of white grapes.

5. Adjust the number of white grapes to match the ratio:
- The ideal ratio is 3 cherry halves for every 8 white grapes.
- Multiply both numbers of the ratio by the same factor to obtain a common multiple.
- To match 4 sets of the ratio (4 x 3: 4 x 8), we multiply 3 and 8 by 4.
- The adjusted ratio becomes 12 cherry halves: 32 white grapes.

6. Modify the number of white grapes in the jar to match the adjusted ratio:
- Currently, there are 20 white grapes in the jar.
- Subtracting the number of existing white grapes from the desired number (32 - 20), we need to add 12 white grapes to the jar.

7. Add the necessary amount of white grapes to the jar:
- To fix the error, 12 white grapes should be added to the jar to match the desired ratio of 12 cherry halves: 32 white grapes.

By adding 12 white grapes to the jar, the company can fix the error and ensure the proper fruit mixture with a ratio of 3 cherry halves to 8 white grapes.