Melvin is building a castle with a series of towers out of blocks. Each tower has twice as many blocks as the previous tower, and then 3 more. If the first tower has x^2 + 2x + 3, and Melvin builds 5 towers in all, how many blocks will he have used in total?

A. 5x^2 + 10x + 15
B. 3x^2 + 6x + 9
C. 16x^2 + 32x + 93
D. 31x^2 + 62x + 171

Question

Melvin is building a castle with a series of towers out of blocks. Each tower has twice as many blocks as the previous tower, and then 3 more. If the first tower has x^2 + 2x + 3, and Melvin builds 5 towers in all, how many blocks will he have used in total?

A. 5x^2 + 10x + 15
B. 3x^2 + 6x + 9
C. 16x^2 + 32x + 93
D. 31x^2 + 62x + 171

anonymous · Answer

5x^2 + 10x = 10x + 10x = 20x? I don't know... but 3 x 5 = 15.

ranga · Answer

Assume the first tower has N blocks. 
Each tower will have TWICE as many blocks as the previous tower PLUS 3. 
1st tower:  N blocks 
2nd tower: 2N + 3 
3rd tower: 2(2N+3) + 3 = 4N+9
4th tower: 2(4N+9) + 3 = 8N+21
5th tower: 2(8N+21) + 3 = 16N + 45

Add all of them: N + 2N+3 + 4N+9 + 8N+21 + 16N+45
Total = 31N + 78

But the first tower has N blocks which is equal to x^2 + 2x + 3 (given).  
Put N = x^2 + 2x + 3 in the Total
Total = 31(x^2+2x+3) + 78 = 31x^2 + 62x + 171

anonymous · Answer

@KellyRjr That is the correct answer ^ - I must have misread the question or something, sorry