Question

Please answer both questions and show all your work. Thank you!!! :)

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?

Answer 1

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

Set up the equations:

`r + c = 1000\\4r + 2c = 3150\\\\-2r -2c = -2000\\4r + 2c = 3150\\\\2r = 1150\implies r = 575\implies c = 425`

Answer: There are 575 rabbits and 425 chickens

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

Set up equations:

`m = 4a\\m-8 = 2(a+8)\\\\4a-8=2a + 16\\2a = 24\implies a = 12\implies m = 48\\`

Answer: Mike has 48 stamps. Andrew has 12 stamps.