Question

Translate the situation into an equation... Alice is twice as old as Lisa and Brandon is four years younger than Lisa. If their average age age is 32, how old is Alice.. Please show steps

Answer 1

Ready to work on this together?

Answer 2

Let me know whenever you're here. We'll get the answer together so that you'll always know how to solve these!

Answer 3

im here

Answer 4

Awesome. Ok, first things first: who are we using as our reference point? In other words, who are we using to compare to the other people? If that question doesn't make sense, I can reword it.

Answer 5

i think Alice

Answer 6

We're actually using Lisa. Notice how we say that alice is twice as old as Lisa, and that brandon is four years younger than Lisa. If we know how old Lisa is, then we'll know how old the other two are. Does that make sense?

Answer 7

yes

Answer 8

Okie dokie. So what we'll do is say that Lisa = x, since she's the 'unknown age that we will use to compare everyone to her"

Answer 9

Remember: lisa is now called "x".

Answer 10

Alice is TWO times older than Lisa, I mean.

Answer 11

ok

Answer 12

Alright, so show me what Alice's age would be represented by.

Answer 13

2x

Answer 14

Perfect!
So we know that lisa = x
and alice is 2x

Now all we have left is Brandon. He is four years younger than Lisa. How do we show this?

Answer 15

-4x

Answer 16

That would actually mean "minus four times". Note that we are just saying he's four years younger, not four times younger.

Answer 17

ok

Answer 18

In other words, "If I have 10 apples, and Trust26 has 4 less apples than me, how do we show this in an equation?"

Answer 19

10 -4

Answer 20

Perfect. So in Brandon's case, we have x-4, right?

Answer 21

ok

Answer 22

Alright! So here's where it gets a little tricky. Imagine I told you to find the average of 10, 4 and 1. What would you do?

Answer 23

Solve the following simultaneous equations for alice, brandon and lisa:
\[\left\{\text{alice}\text{=}2\text{ lisa} ,\text{brandon}=\text{lisa}-4,\frac{\text{alice}+\text{brandon}+\text{lisa}}{3}\text{=}32\right\} \]

Answer 24

^ I think that might be a little tricky for an algebra 1 student.

Answer 25

O am not for sure Uber

Answer 26

You would add all three first, right?

Answer 27

10 + 4 + 1 = 15

Answer 28

Now, what is the second step?

Answer 29

ok imma lost where did you get 10+4+1 from

Answer 30

Oh, that's just an example I'm making to show you what you will do later.

Answer 31

I'm checking to make sure you know how to average stuff before we go back to the problem itself. The 10,4,1 are just made up numbers I'm going to use to show you the steps for making an average.

Answer 32

ok. i got you. go ahead

Answer 33

Alright. So do you know what you do after you get 15?

Answer 34

divide

Answer 35

Excellent. By what number?

Answer 36

\[\{\text{alice}\to 50,\text{brandon}\to 21,\text{lisa}\to 25\} \]

Answer 37

3

Answer 38

Exactly. So we'd have (10+4+1)/3 = 5, where 5 is the average.

Now... we're going to do the same thing for your original question.

Answer 39

ok

Answer 40

( )/[ ] = {}

Our formula will look like that, kinda. Do you see how the blanks match the "(10+4+1)/[3] = {5}" question?

Answer 41

yes

Answer 42

Alice is twice as old as Lisa and Brandon is four years younger than Lisa. If their average age age is 32, how old is Alice

Answer 43

Ok, so what do we put in the ( ) ?

Answer 44

Hint: the ( ) in our first example was 10 + 1 + 4

Answer 45

we put their ages in the ( )

Answer 46

Exactly! So here's what we had:
(Alice + Lisa + Brandon)
(x + 2x + x-4)

So far so good?

Answer 47

yes

Answer 48

Okie dokie. First thing we should do is simplify the junk in there. What would we get after combining like terms? (x + 2x + x-4)

Answer 49

4x-4 than divide 4x/4 and 4/4

Answer 50

It's better if we just leave it at 4x-4 to be honest. We shouldn't divide anything until we have something in the form of 4x-4 = "something".

So, we have (4x-4)/[] = {}

Answer 51

How many people do we have?

Answer 52

3

Answer 53

Excellent. So we have (4x-4)/3 = {}

What goes in the {}?

Answer 54

Alice is twice as old as Lisa and Brandon is four years younger than Lisa. If their average age age is 32, how old is Alice..

Answer 55

50

Answer 56

We'd actually put in 32, as that was the answer to our average.

Answer 57

(4x-4)/3 = 32

Make sense?

Answer 58

ok ok yes i see

Answer 59

Awesome. So here's the next part: we want all our X's to be on one side, and our other numbers on the other. Do you know how we can get rid of the /3 first?

Answer 60

Here's a hint:

If I had 10/2 = 5, how do I move the 2 to the other side while still making it a true statement?

Answer 61

(That's another random example not directly related to our equation, by the way)

Answer 62

add whats in the ( ) first

Answer 63

Well, we can't get any deeper than (4x+4)

Answer 64

Try that other example first. 10/2 = 5

How do we move the 2 to the right and still let it be true?

As in... 10 = 2 [] 5

Answer 65

What mathematical symbol goes in that []

Answer 66

divide

Answer 67

Careful.

Answer 68

10 = 2/5 is not true

Answer 69

ok

Answer 70

So 5 [what] 2 = 10? +? -? /? *?

Answer 71

o times

Answer 72

excellent.

Answer 73

So remember: If you ever have something like a/b = c, and you need to get a by itself, just move the b to the right and times it. So in this case, a = b * c. Makes sense?

Answer 74

yes it does

Answer 75

Awesome. (4x-4)/3 = 32
How do we make the 3 go to the other side?

Answer 76

(Don't worry. We're *almost* done.)

Answer 77

just move it

Answer 78

Yup. And what else?

Answer 79

and times it

Answer 80

Exactly. So what do we get? (4x-4)/3 = 32

Answer 81

(4x-4)= 32*3

Answer 82

Excellent. So 4x-4 = 96
4x = 100
x = 25

Did these steps make sense?

Answer 83

yes

Answer 84

yes

Answer 85

Translate the situation into an equation... Alice is twice as old as Lisa and Brandon is four years younger than Lisa. If their average age age is 32, how old is Alice.. Please show steps

Answer 86

So, is 25 our final answer?

Answer 87

ok i ok see no cause you have to time it by two

Answer 88

ok i ok see no cause you have to time it by two

Answer 89

Perfect! So, 50. :)

Good work.

Answer 90

o thank yoou for the help you deserve a medal to and i am going to give it to you. beacsue you actually took time out to teac me

Answer 91

Yay :D

Answer 92

And thank YOU for trying to solve unlike some folks that just say "No. It's too hard. I give up." :D