How many sacks are there?

Question

Sacks of flour are stored in piles. The bottom layer has 20 sacks along its length and is 4 sacks wide. Each Layer above has one less sack lengthwise than the previous layer but the same width. The top layer has 16 sacks. How many sacks are there altogether in the pile?

Answer 1

There are two possible readings of this: either the top layer has 16 sacks LENGTHWISE, or the top layer actually has 16 sacks (four wide x four long).

As someone else has worked the first reading (correctly!), I'll take the second:

One trapezoidal face of the pile, along the length, has

20+19+18+17+16+15+14+13+12+11+10+9+8+7... sacks.

Looking for a lazy way to add this, I notice that this is equal to the triangular number of order 16 (the sum of the numbers 1 through 16) plus 17 fours. That triangular number can further be simplified to

(1+16) + (2+15) + (3+14) + ... + (7+10) + (8+9), so it's equal to eight 17s. The whole face therefore contains 12*17 sacks, and since the entire pile is four sacks wide, there are

4 * 12 * 17 = 816 sacks

Answer 2

4(20 + 19 + 18 + 17 + 16) = 4(90) = 360 sacks

Answer 3

4(20+19+18+17+16+15+14+

13+12+11+10+9+8+7+6+5+4)

=4(204)=816 sacks,

assuming you meant a total of 16 sacks on the top, not 16*4.

If you were talking 16*4 on the top, then it would be:

4(20+19+18+17+16)=4(90)=360 sacks.

Answer 4

The basic formula is the summation of all the sacks on each layer:

L(n1) = 20, W(n1) = 4

L(n2) = 19, W(n2) = 4

L(n3) = 18, W(n3) = 4

L(n4) = 17, W(n4) = 4

L(n5) = 16, W(n5) = 4

Since the width for all the layers is the same, we will simplly refer to the width with W = 4.

The formula for the sum is reduced to

S(L,W) = W (L(n1) + L(n2) + L(n3) + L(n4) + Ln5)

Substitute the values and calculate the result:

S(L, W) = 4(20 + 19 + 18 + 17 + 16)

S(L, W) = 360

Answer 5

Bottom layer --> 4 x 20 = 80

Next layer --> 4 x 19 = 76

Next layer --> 4 x 18 = 72

Next layer --> 4 x 17 = 68

Next layer --> 4 x 16 = 64

Total = 5 x 72 = 360 sacks

Answer 6

there is 360 sacks

Answer 7

Total bags = 4(20 + 19 + 18 + 17 + 16)

= 4 × 90 = 360 bags

--------