3 bars of length 16, 20 and 24 cm are cut into equal parts and are packed in a box which can contain maximum of two pieces of such rods. Find the minimum number of boxes required.
Question
3 bars of length 16, 20 and 24 cm are cut into equal parts and are packed in a box which can contain maximum of two pieces of such rods. Find the minimum number of boxes required.
Solution
To solve this problem, we first need to find the greatest common divisor (GCD) of the lengths of the bars, which are 16, 20, and 24 cm. The GCD will give us the length of the equal parts into which the bars can be cut.
The GCD of 16, 20, and 24 is 4 cm. This means that each bar will be cut into pieces that are 4 cm long.
Next, we calculate how many pieces each bar will be cut into:
- The 16 cm bar will be cut into 16/4 = 4 pieces.
- The 20 cm bar will be cut into 20/4 = 5 pieces.
- The 24 cm bar will be cut into 24/4 = 6 pieces.
So, in total, we will have 4 + 5 + 6 = 15 pieces.
Since each box can contain a maximum of two pieces, we will need 15/2 = 7.5 boxes. However, since we can't have half a box, we will need to round up to the nearest whole number.
Therefore, we will need a minimum of 8 boxes to pack all the pieces.
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