Answer both questions and show all your work. ! : ) 1) there are 1000 rabbits and chickens on a farm and together they have 3150 legs. how many rabbits and how many chickens are there on the farm? 2) mike has 4 times as many stamps as andrew. if mike gives andrew 8 stamps, he will have twice as many stamps as andrew. how many stamps does each boy have?

(1) let "r" denote number of rabbits, "c"  number of chickens

Set up the equations:

There are 575 rabbits and 425 chickens

(2) m - number of Mike's stamps, a - number of Andrew's stamps.

Set up equations:

 Mike has 48 stamps. Andrew has 12 stamps.

Given:

Consider the below table attached with this question.

Every square meter of ceiling requires 10.75 tiles.

To find:

The missing values in the table.

Solution:

We have,

1 square meter of ceiling =  10.75 tiles.      ...(i)

Therefore, the number of tiles corresponding to 1 square meter of ceiling is 10.75.

Multiply both sides by 10.

10×1 square meter of ceiling =  10×10.75 tiles.

10 square meter of ceiling =  107.5 tiles.

Therefore, the number of tiles corresponding to 10 square meter of ceiling is 107.5.

Divide both sides by 10.75 in (i).

square meter of ceiling = 1 tile.

Multiply both sides by 100.

square meter of ceiling = 100 tiles.

On approximating the value, we get

9.3 square meter of ceiling = 100 tiles.

Therefore, the square meters of ceiling corresponding to 100 tiles is about 9.3.

Multiply both sides by a in (i).

a×1 square meter of ceiling =  a×10.75 tiles.

a square meter of ceiling =  10.75a tiles.

Therefore, the number of tiles corresponding to a square meter of ceiling is 10.75a.