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20 July, 06:10

You are tasked with building a tower of blocks exactly 10 cm high. You have two types of block to work with. Each block A is 2 cm high, and each block B is 3 cm high. You may use any number of each type of block, and may stack any kind of block on top of any other kind. How many possible towers are there

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  1. 20 July, 08:02
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    2 possible towers

    Step-by-step explanation:

    2 possible towers

    Step-by-step explanation:

    The height of the tower required is 10 cm, and that height may be obtained by 'x' number of blocks A and 'y' number of blocks, knowing its respective height, so 'x' and 'y' must accomplish the equation:

    [tex] 10 = 2x + 3y [ / tex]

    The maximum value for 'x' is 5; a higher value will give a higher than 10 cm height as a result. So, the possible answers for 'x' are: (0,1,2,3,4,5). Note that both 'x' and 'y' values must be integers, and the only numbers that satisfy that condition are (x = 2, y = 2) and (x = 5, y = 0). The other options for 'x' will give a noninteger value for 'y' because of the equation above.

    So, there are just two options.
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