Question

Part A: Solve A = 9 over 2(x + 28) for x.
Part B: Determine the value of x when A = 135.
Part C: Solve –np – 40 > 10 for n. Show your work.

Answer 1

\[A= \frac{ 9 }{ 2 } \left( x + 28\right)\]

Answer 2

@zepdrix can you help me with this?

Answer 3

part A: "solve for x" means we want to get x by itself

start by multiplying both sides of the equation by 2 to eliminate the denominator

Answer 4

A2=? (x + 28)

Answer 5

\[\large\rm A=\frac{9}{2}\left(x+28\right)\]Multiplying both sides by 2 gives you,\[\large\rm 2\cdot A=2\cdot\frac{9}{2}\left(x+28\right)\]Don't think of that 2 as a denominator, think of the operation being performed.
It's actually division by 2.
So we're multiplying and dividing by 2 on the right side of the equation.
Those actions will "cancel out".\[\large\rm 2\cdot A=\cancel{2}\cdot\frac{9}{\cancel{2}}\left(x+28\right)\]

Answer 6

Which puts you here,\[\large\rm 2A=9(x+28)\]

Answer 7

divide by 9 and then subtract 28? @zepdrix

Answer 8

\[\frac{ A2 }{ 9 }-28=x\]

Answer 9

Ahh sorry had to go make some food +_+

Answer 10

Looks good!

Answer 11

2! the answer to B it x = 2!

Answer 12

yay good job \c:/

Answer 13

:DD

Answer 14

-np - 40 > 10

add 40 first or...

Answer 15

Yah, that seems like a good first step

Answer 16

-n > 50/p

but what about that minus sign?

Answer 17

I guess you'll want to divide each side by -p, not simply p.

Do you remember what happens when you divide a negative across an inequality?

Answer 18

the inequality flips

Answer 19

yessss

Answer 20

n < 50/-p

Answer 21

Ok great!
Let's bring the negative sign out front because
\(\large\rm \frac{50}{-p}\) is the same as \(\large\rm \frac{-50}{p}\) which is the same as \(\large\rm -\frac{50}{p}\).

It doesn't really matter where the negative goes, it just looks nicer in front like this form.

Answer 22

ok. do you have time for one more question?

Answer 23

sure!

Answer 24

Bruce has a bottle that contains 60% of lemon juice and the rest water. The bottle has 1 liter of water.

Part A: Write an equation in one variable that can be used to find the total number of liters of lemon juice and water in the bottle. Define the variable used in the equation.

Part B: How many liters of lemon juice are present in the bottle? Show your work.


This one is really confusing to me.

Answer 25

Mmm I remember this one coming up like 6 months ago, confused me also lol
gimme a sec XD

Answer 26

ok :)

Answer 27

im not so smart

Answer 28

Oh oh oh oh oh.. ok now I remember why I got confused on this one.
Make sure you understand the second sentence.

It's NOT saying that bottle contains 1Liter of liquid.
It contains 1Liter of water. They're not telling us how much total liquid is in the bottle.

Answer 29

So umm

Answer 30

Ok, i see how that can get you!

Answer 31

Ok if lemon juice accounts for 60% of the liquid in the bottle,
what % does that leave for water?

Answer 32

40%

Answer 33

Good good good. and I think we can use thattttt :)
sec, brain ... not... working lol

Answer 34

lol

Answer 35

The `amount` of water is 1Liter.
So this 1Liter accounts for 40% of the total Liquid in the bottle.

\(\large\rm 1L=.40T\)
So how much total liquid is in the bottle?
Can you solve this algebraically? (Ignore the L, that's just a unit).

Answer 36

Darude-Sandstorm

Answer 37

1.40L

Answer 38

t

Answer 39

Woops! The 40% is `multiplying` the Total.
So to isoluate your total, T, you'll need to divide.

Answer 40

isolate*

Answer 41

2.5

Answer 42

Good good good.
We've determined that the total amount of liquid in the bottle is 2.5Liters.

The lemon juice accounts fo 60% of that total.
So we can again set this up algebraically:\[\large\rm \ell=.60T\]And since we've solved for the total, T, we can plug it right in,\[\large\rm \ell=.60\cdot 2.5\]And solve for l, the amount of lemon juice in the bottle.

Answer 43

Do those steps.... kinda make sense? 0_o
It's a tricky problem to get through.

Answer 44

1.5

Answer 45

1.5=.60*2.5

Answer 46

Good! :)

So there is:
1Liter of water which is 40% of the total liquid
1.5Liter of lemon juice which is 60% of the total liquid

2.5Liters of total liquid which is 1 + 1.5

Answer 47

Yayyy I think we did it \c:/

Answer 48

Thank you so much for all your help today! I really understand it better too.

Answer 49

np \c:/ yay team!