Question

Bonnie has a container in the shape of a rectangular pyramid. The formula for the surface area of the enclosed space is S = lw + 0.5Ph. Solve for P.

P = S – lw – 0.5h
P = S + lw + 0.5h
P = The quantity S minus l times w all divided by 0.5 times h
P = S divided by the quantity l times w plus 0.5 times h

Answer 1

@alivejeremy

Answer 2

you start with
S = lw + 0.5Ph

we want "P" by itself on one side.
I would first "move" the term lw to the other side
lw (or l*w or l times w) can be thought of as some number
if you subtract it from the right side (and the left side to keep things equal)
you have
S- lw = lw - lw + 0.5Ph

any idea what lw - lw simplifies to ?

Answer 3

are those the answers

Answer 4

thats confusing...

Answer 5

thats confusing @phi

Answer 6

OK, if it's confusing, that means you are missing an idea
to figure out what idea you need to learn, do you know how to solve for P with
S= 2+P
?

Answer 7

i think

Answer 8

how ?

Answer 9

u cant do it

Answer 10

Yes we can

Answer 11

solve means "have P on one side, by itself"

Answer 12

How do we isolate p

Answer 13

how? im like so lost

Answer 14

you have to subtract 2 from both sides

Answer 15

ok how about
5= 2+ P
can you get "P" by itself ?

Answer 16

S= 2 + p by phi
Solve for p
P is having 2 added to it
So we can get rid of 2 by reversing the operation. What's the opposite of adding?

Answer 17

yes @phi
subtacting @will.h

Answer 18

Great
So subtract 2 from both sides
S - 2 = 2 - 2 + p
The right side can be simplified 2-2 is zero so that would leave only p
S-2 = p

Your original problem can be solved just like this

Answer 19

Here are the two ideas you need to solve for P in
5= 2+p

1) 2 - 2 = 0 (which makes it "go away")
so if on the right side we do 2- 2 + p
the 2-2 becomes 0 and 0+p= p because adding 0 does not change anything

2) if we do -2 on one side, we *must* do the same on the other side, to keep things equal

Answer 20

does that part make sense ?

Answer 21

ok @phi @Will.H

Answer 22

as a test, can you "solve for p" in
6= 1+P
?

Answer 23

like that?

Answer 24

ok. next idea:

anything minus itself is zero

that is an important idea.

Answer 25

we use that idea in
5= x+P
how do we "solve for P" ? what do we subtract from both sides ?

Answer 26

is this part confusing ?

Answer 27

we subtract x

Answer 28

but i dont know how

Answer 29

with letters it's easier than with numbers. you write -x on both sides
which means "subtract x"

example:
5= x+P
5-x = x-x+P

Answer 30

ok

Answer 31

we can't "simplify" 5-x (it stays that way)
but on the right side, we know x-x is 0
because anything (which includes "x") minus itself is 0
so we can simplify it to
5-x = 0+P
and (I think you know) adding 0 can be ignored (or rather 0+ whatever = whatever)
so we get
5-x= P

Answer 32

ok and how does this help with my math problem?

Answer 33

what to try solving for P in
S= lw + P
?

(lw means l*w, but we can subtract lw from both sides)

Answer 34

*want (not what)

Answer 35

yes
so p=lw-s

Answer 36

yes. so we are getting there!

Answer 37

ok so whats next?

Answer 38

the original problem is
S = lw + 0.5Ph

we know how to subtract lw from both sides to get
0.5Ph = S-lw (I switched the left and right sides, but we can do that)

Answer 39

ok
so now im confused

Answer 40

let me do it slower
S = lw + 0.5Ph

add -lw to both sides (we write -lw on both sides)
S-lw = lw - lw + 0.5Ph

simplify lw - lw to 0
S-lw = 0 + 0.5Ph

next simplify 0+0.5Ph to 0.5Ph (adding 0 is ignored)
S-lw= 0.5Ph

ok ?

Answer 41

ok

Answer 42

and
S-lw= 0.5Ph
can also be written
0.5Ph = S-lw

Answer 43

so the answer is A?

Answer 44

I assume you know if
A=B
then B=A
i.e. in an equation, we can write it either way.
usually, we write it so the variable we are "solving for" is on the left side
so before continuing, we write
S-lw= 0.5Ph
as
0.5Ph = S-lw

Answer 45

the next idea
this one is as important as anything minus itself is zero

IDEA: anything divided by itself is one

examples: 2/2 is 1
5/5 is 1
x/x is 1

xy/ xy = 1
and so on

Answer 46

ok so its b?

Answer 47

we have
0.5Ph on the left side
that means
0.5 * P *h (they are being multiplied)

we can change the order of multiply (example 2*3 is the same as 3*2)
in this case, write it as
0.5*h * P
now we divide this by 0.5*h, like this
\[ \frac{0.5\cdot h \cdot P}{0.5\cdot h} \]
or (if you know how fractions work)
\[ \frac{0.5\cdot h }{0.5\cdot h} P\]

Answer 48

notice we have 0.5h divided by itself
that means we get 1

and the left side 0.5hP/(0.5h) = 1*P= P (1 times anything is the anything)

but to keep things equal we have to divide the other side by 0.5h

Answer 49

in other words we do
\[ \frac{0.5Ph}{0.5h}= \frac{S-lw}{0.5h} \\
P= \frac{S-lw}{0.5h} \]

notice I did not rearrange the top from 0.5Ph to 0.5h P because I know the 0.5 divides with the 0.5 in the bottom and ditto for the h

Answer 50

ok

Answer 51

so whats the answer? now im confused

Answer 52

read the last post carefully

Answer 53

Its C?

Answer 54

which of your choices matches what I posted ?

yes, choice C (if you wrote it as an equation instead of in words)

Answer 55

ok