Desperate for the answer

if i give my sister 5 dollars, then we will have the same amount of money. if instead she gives me 8 dollars, then i'll have twice as much money as she has. how much money does she
have?

Let X = the amount you have and Y = the amount she has.

If you give her 5 you would have the same amount so you get an equation like:

X-5 = y +5

Simplify :

X – y = 5+5

X -y = 10  (Call this equation 1).

Now if she gives you $8 you will have twice as much as her, so set up the second equation:

2(y-8) = x +8

Simplify:

2y -16 = x +8

2y -x = 8 +16

2y -x = 24 (Call this equation 2).

Now add equation 1 and 2 together:

X – y = 10 + 2y -x = 24

Simplify to get y = 34

Now replace y with 34 in equation 1 to solve for x:

X -34 = 10, x = 44

You have $44 and your sister has $34

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below:

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!