world problem

Question

lebles will be cut from a sheet of paper that measures 9 inches by 12 inches. lf each label need to be 2 1/4 inches by 1/1/3 inches, how many labels can be cut from that sheet of paper?

Answer 1

the dimensions of each label are 4/3 in by 9/4 in.

 

I.  Consider placing the labels side by side running across the paper width, 9 inches.  how many? n(4/3) ≤ 9; so maximum n = 6.75, rounded down to 6 (no partial labels allowed). 

Going down the length (12"), there are m rows of labels; m(9/4) ≤ 12 so m maximum = 48/9 = 5.333; maximum m is 5.

Thus 6 times 5 = 30 labels, in this option.

 

II. Placing labels along the paper length, 12".  n(4/3) ≤ 12; n ≤ (3/4)(12) = 9

Going down (9"), m (9/4) ≤ 9; maximum m = 4.  Thus 4 times 9 = 36 labels, in this option.

 

Final answer: 36