 Mathematics
15 August, 17:01

# 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

+2
1. 15 August, 17:03
0
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.