Question

Jodi is cutting out pieces of paper that measures 8 1/2 inches by 11 inches from a larger sheet of paper that has an area of 1000 square inches. What is the greatest possible number of pieces of paper that Jodi can cut out of the larger sheet?

Answer 1

This is easy, just divide 1000 by 8.5 your answer will be 117.

Answer 2

9

Explanation:

The possible dimensions of the larger piece of paper that could give us 1000 square inches for area are:

1×1000; 2×500; 4×250; 5×200; 8×125; 10×100; 20×50; 25×40

We want to use dimensions that will allow us to cut 8 1/2 by 11 sheets. This means that the smallest dimension needs to be larger than 8 1/2 inches; this leaves us with

10×100; 20×50; 25×40

For the first one, 10×100, we can have 1 row across the 10 inch dimension, and 100/11 = 9 columns across the other dimension. This gives us 1×9 = 9 sheets.

For the 20×50, we can have 2 rows across the 10 inch dimension and 50/11 = 4 columns; this gives us 2×4 = 8 sheets.

For the 25×40, we can have 2 rows across the 25 inch dimension (we lack half an inch of having 3) and 40/11 = 3 columns; this gives us 2×3 = 6 sheets.

The largest number of sheets was 9.