Bob had some blue balloons and green balloons in the ration 4:5. He gave away 12 blue balloons and 12 green balloons. Then the ratio of the number of blue balloons to the number of green balloons he had left became 5:7. How many blue balloons did Bob have at first?
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Question
Answer
Blue | Green | |
Before | 4 units | 5 units |
Change | -12 | -12 |
After | 5 parts | 7 parts |
Multiply Blue’s column by 7 and Green’s column by 5 to get equal parts:
Blue | Green | |
28 units | 25 units | |
-84 | -60 | |
35 parts | 35 parts |
Comparing the two columns:
28 units – 84 = 25 units – 60
3 units = 24
1 unit = 8
Blue balloons at first = 4 units
= 4 × 8
= 32
This is a problem sum dealing with a concept called Constant Difference.
This means that the difference between the blue and green balloons should remain the same for the ‘before’ situation and the ‘after’ situation. This is because an EQUAL amount of blue and green balloons were given away. This causes the difference between the different colours to remain the same. Likewise, the difference will remain the same if Bob receives an EQUAL amount of blue and green balloons from someone else.
Looking at the solution provided, we can see that the difference in the ‘before’ is 1 unit while the difference in the ‘after’ is 2 units. Remember, that the difference should remain the same as this is a Constant Difference question. So, we make it the same by doing some manipulation to the ratio of ‘4 : 5’, and change it into its complex form ‘8 : 10″, so that now we can observe that the difference for the ‘before’ is 2 units, just like the ‘after’.
By observation, we can compare the two ratio we have now obtained, ‘8 : 10’ and ‘5 : 7’. We can see that each colour has its units decreased by 3 units. This shows us that these 3 units corresponds to our value of 12 balloons of each colour. So, 3 units represents 12 balloons, 1 unit represents 4 balloons.
To answer the question, there were 8 units of Blue balloons at first, so that makes it 32.
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