2. pb and j array ken has made a selection of square jam sandwiches for party, which he arranges in a single layer on the table in perfect rectangle. sarah has brought along the same number of square peanut butter sandwiches, which she puts out, also as a single layer, to form a border va (one sandwich wide) around ken's given that all of the sandwiches are the same size and they are all used, how many sandwiches could each person possibly have made?

Let's assume Ken arranged his sandwiches in a rectangular shape with length 'L' and width 'W'. Now Sarah arranged her sandwiches to form a border around Ken's rectangle. The solution diagram is attached below.

Ken needs as much sandwiches as area of rectangle i.e. number of Ken's sandwiches would be = LW.

It is clear that Sarah needs as much sandwiches as perimeter of rectangle and extra four sandwiches to put on corners. It means number of Sarah's sandwiches would be = 2·(L+W) + 4.

Given that all of the sandwiches are the same size and they are all used.

Ken and Sarah bought same number of sandwiches. So we need to solve the following equation :-

Number of Ken's sandwiches = Number of Sarah's sandwiches

LW = 2·(L+W) + 4

Using trial and error approach, we get 6 x 4 = 2 x (6 + 4) + 4.

So number of Ken's sandwiches would be LW = 6 x 4 = 24 sandwiches.

Hence, final answer is "Each person could have 24 sandwiches".

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.