Question

Does anyone know how to set the problem up?
In the savannah, a sinkhole opened up catching some ostrich and cheetah. There was a total of 13 animals to be rescued. If 44 individual feet were pulled from the muck, how many ostrich and how many cheetahs were rescued?

Answer 1

you have to count feet, knowing that ostriches have 2 feet and cheetah's have 4 feet

first step: set up an equation for the number of feet if you have x ostriches and y cheetahs

Answer 2

9 cheetah and 4 ostrich

Answer 3

x(2)+y(4)=44?

Answer 4

and one more equation.. can u guess ??

Answer 5

yes
now an equation for the number of animals if you have x ostriches and y cheetahs.

Answer 6

hmmmm. i honestly have no idea

Answer 7

x+y gives 13

Answer 8

think about it: you have x ostriches and y cheetahs.

Answer 9

but i just made an equation with x and y?

Answer 10

that's ok, you can make another one (if fact, that is the point)
your first one was about feet. this next one is about heads (everybody has only one head)

Answer 11

oh so x+y=44?

Answer 12

44 is the number of feet. look at the problem.

Answer 13

x+y=13

Answer 14

does that make sense?

Answer 15

yes! thankyou. no could tell me how to set it up? would i put the first equation over the second one or solve them separately?

Answer 16

*now

Answer 17

we have 2 equations and 2 unknowns (we always need as many equations as unknowns)

2x+4y=44
x+y= 13

I would multiply the bottom equation by -2
(that means multiply every term on both sides of = by -2)
what do you get?

Answer 18

then add the two equations.

Answer 19

2x=4y=44
-x^2+-y^2= -26?

Answer 20

multiply like this: put a -2* in front of every term
what do you get?

Answer 21

-2x+-2y+ -26?

Answer 22

ok, but you left out the = sign

so what we now have is
2x+4y=44
-2x+-2y= -26

Answer 23

now add the 2 equations. the easy way is just write down all the terms on one line on the left side of the = and on the right side

Answer 24

I added and got 18

Answer 25

that is the right side. do the same thing for the left side. and you should write down the whole equation (less chance of making a mistake)

Answer 26

the right side?

Answer 27

like this:
2x+ 4y= 44
-2x+-2y= -26
-------------
2x-2x+4y+ -2y= 44-26

now simplify. the right side (as you know) is 18
can you simplify the left side?

Answer 28

x cancels out i think and then you have
2y=18
/2 /2
y=9 but whatdoes x equal?

Answer 29

looks good. now go back to the original equations

2x+4y=44
x+y= 13

pick one of them (does not matter which, except the 2nd one looks simpler)
replace y with 9

Answer 30

x+y= 13
x+9=13
-9 -9
x=4
THANKYOUSO MUCH FOR ALL YOUR HELP :)

Answer 31

yw. look over how we did it. do you see why we multiplied the 2nd equation by -2 before adding the 2 equations? (to make the x's cancel out)
so one of the tricks is seeing that -2 works.