Quantity

[Guest]

A quantity of bolts are to be produced from a bar of 3/4" square stock 8 1/4' in length. Allowing 1/8" for waste in cutting off each bolt, calculate number of bolts that can be made.

Illustration of bolt attached.


My attempt at solution:

8 1/4' = 99"

2 5/8" - 1/8" = 2 4/8" = 2.5"

99 / 2.5 = 39.6 = 40 bolts.

Where am I correct ?

[Guest]

Let number of bolts = B
Then number of cuts = B-1

Bx(2 5/8) + (B-1)x(1/8) = 99

Multiply across by 8 to get rid of fractions

21B + B - 1 = 792
22B = 793
B = 793 / 22 = 36.05 bolts = 36 bolts able to be cut ....
...and we have to cut 1/8 inch off the last bolt, so actually B cuts made.

OR ....length of bar used for each bolt = 2 5/8 plus 1/8 for cut.

2 5/8 + 1/8 = 2 3/4 = 11/4

B x 11/4 = 99

B x 11 = 99 x 4

B = 99 x 4 / 11 = 36

[Guest]

Thanks.

A question from the first solution:

Why are the number of cuts B - 1 ?

[Guest]

If the length of the bar was exactly the the length for a whole number of bolts without a piece left over, then say for 10 bolts there would be 9 cuts
Same as fence posts for 4 posts you have 3 spaces in between.

[Guest]

I understand now. Thanks again.

[leesajohnson]

8 1/4' = 99"

2 5/8" + 1/8" = 23 /4" = 11/4"

B x 11/4 = 99
99 x 4 / 11 = 36