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

Question

Mathematics

Arnav Beard

19 September, 02:02

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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Anne Harris · Answer 1

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.