Question

1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
(a) Write an equation that represents the situation. Explain any variable used.
(b) Solve the equation from Part (a). Show your work. State your solution as a complete sentence.
Answer:
 

Answer 1

who ever answers gets a medal

Answer 2

Let K = Kim's age
Let S = Her sisters age

\[K = 2S\]
\[K + S = 36\]

Answer 3

Do you understand how I got those equations?

Answer 4

a little bit are those the answers

Answer 5

Haha, the above equations and definitions of the variables, answer only part a

Answer 6

What do you think we should do now, going from here?

Answer 7

slove it

Answer 8

How?

Answer 9

36 -2

Answer 10

How did you get that?

Answer 11

becuase you had 2S and then there was 36

so i did 36-2
but now i know its wrong by looking at it

Answer 12

Ok, we want to solve for K and S, because the question is asking "How old is each sister?"

Answer 13

umm

Answer 14

Remember how we defined each variable

Let K = Kim's age
Let S = Her sisters age

Then set up the equations

\[K = 2S\]
\[K + S = 36\]

We have setup a system of equations, comparing the two variables. There are two algebraic methods you can use to solve for this type of problem. Have you heard of elimination or substitution before?

Answer 15

i think so

Answer 16

Which one have you heard of, and do you have an idea of how you are supposed to start it?

Answer 17

no

Answer 18

Lets go with substitution, as it is the easiest one to learn.

Basically, substitution is when you solve for one variable, using the equations, to solve for the other one.

First, we want to isolate one variable, and use what it is equal to.

We have,

\[K = 2S\]
and
\[K + S = 36\]

Since K = 2S, we can substitute 2S, for K, in the equation
\[K + S = 36 \rightarrow 2S + S = 36\]

Answer 19

k

Answer 20

Add like terms

\[3S = 36\]

Isolate the variable, S, by dividing the equation by 3

\[S = 12\]

Therefore we know that the sisters age is 12.
Now we need to solve for Kim's age.
Luckily we already have an equation that equals her age

\[K = 2S\]

We know that,
\[S = 12\]

Therefore we input...
\[K = 2(12)\]

Distribute 2, to 12(multiply 2 by 12)

\[K = 24\]

Answer 21

We have,

S = 12
and
K = 24

Lets check our work using the equations

\[K = 2S\]
\[24 = 2(12)\]
\[24 = 24 \]

True

\[K + S = 36\]
\[24 + 12 = 36\]
\[36 = 36\]

Answer 22

Now we know for sure, that Kim's age is 24, and her sisters age is 12.

Answer 23

ok so the answer is

Answer 24

(a)

K = Kim's age
S = Her sister's age

K = 2S
K + S = 36

(b)

Show the work that I showed you

Then use this sentence
"Kim's age is 24, and her sisters age is 12."

Answer 25

Do you understand?

Answer 26

Follow these steps, I gtg :P