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In an competition, first, second and third prizes comprise of colour pencils in sets of 30,25 and 20. How many minimum of pencils are required to make sets of 1st, 2nd or 3rd prize?
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In an competition, first, second and third prizes comprise of colour p...
Minimum Number of Pencils Required for Prize Sets

Calculating the Minimum Number of Pencils
To determine the minimum number of pencils required to make sets for the first, second, and third prizes, we need to consider the largest set first, which is the first prize set of 30 pencils.
- First prize set: 30 pencils
- Second prize set: 25 pencils
- Third prize set: 20 pencils

Considering the Third Prize Set
For the third prize set of 20 pencils, we need to ensure that we have enough pencils to cover this set. Since the second prize set has 25 pencils, we already have enough pencils to cover the third prize set as well.

Considering the Second Prize Set
Moving on to the second prize set of 25 pencils, we need to ensure that we have enough pencils to cover this set. Adding the 25 pencils from the second prize set to the 30 pencils from the first prize set gives us a total of 55 pencils.

Considering the First Prize Set
Finally, for the first prize set of 30 pencils, we already have 55 pencils from the combination of the first and second prize sets. Therefore, the minimum number of pencils required to make sets for the first, second, and third prizes is 55 pencils.
By ensuring we have at least 55 pencils, we can create sets for all three prize categories without running out of pencils.
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In an competition, first, second and third prizes comprise of colour pencils in sets of 30,25 and 20. How many minimum of pencils are required to make sets of 1st, 2nd or 3rd prize?
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