How many soccer balls will be needed to build a display 10 levels high?

Question

the chart that is used for this problem has two sides. The left is labeled “Level,x” at the top with the numbers 1,2,3,4,5,6 underneath. On the right side it is labeled “Total number of soccer balls,y” with the numbers 1,4,10,20,35,and 56 underneath.

How many soccer balls will be needed to build a display 10 levels high??

Answer 1

The relationship is cubic

ax³ + bx² + cx + d = y

Substituting 1, 2, 3, and 4

1) a + b + c + d = 1

2) 8a + 4b + 2c + d = 1

3) 27a + 9b + 3c + d = 4

4) 64a + 16a + 4c + d = 20

Subtracting 1 from 2

5) 7a + 3b + c = 3

Subtracting 2 from 3

6) 19a + 5b + c = 6

Subtracting 3 from 4

7) 37 a + 7b + c = 10

Subtracting 5 from 6

8) 12 a + 2b = 3

Subtracting 6 from 7

9) 18a + 2b = 4

Subtracting 8 from 9

6a = 1

a = 1/6

Now substitute a and determine b, c, and d.