Question (Balloons)
String of 2 big balloons is 90cm.,
String of 5 small balloons is 1.2m.,
If both strings are of the same length, there would be 105 more small balloons than the big balloons.
How many balloons are there altogether?
Solution
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The first step is to find the LCM of 90 and 120 to get the common length that the two sizes of balloons can have.
ReplyDeleteTherefore, LCM = 360. (Have omitted the steps to get that)
Therefore, the Big balloon string which has a length of 90 cm would need 4 sets of such to get 360 cm, giving a total of 4 x 2 = 8 balloons.
the Small balloon string which has a length of 120 cm would need 3 sets of such to get 360 cm, giving a total of 3 x 5 = 15 balloons.
Since there are 105 small balloons as compared to big balloons, we have to see how many sets of 15 small balloons and 8 huge balloons are there to get this situation:
105/ (15-8) = 15 sets
Hence total number of balloons = 15 x 8 + 15 x 15 = 345 balloons