Question

A large emerald with a mass of 378.24 grams was recently discovered in a mine. If the density of the emerald is 3.91 grams over centimeters squared, what is the volume?

Answer 1

set up a ratio

378.24g/x cm^3 = 3.91g/1cm^3

now solve for x

Answer 2

I don't know how...

Answer 3

x = the volume 378.24g takes up

Answer 4

are you unfamiliar with basic algebra? If so I can tell you the rules you need to apply?

Answer 5

I was never good at algebra.

Answer 6

to solve the problem,

I'm just making the assumption that the density is equal to 378.24g/x cm^3 of the material, this makes sense based on the simple rule:

\[\frac{x}{y} = \frac{a*x}{a*y}\]

where,

\[\frac{a}{a} = 1\]

where, a = any number other then 0

Answer 7

so for example.

\[\frac{2}{4} = \frac{2*5}{4*5} = 1*\frac{2}{4}\]
because
5/5 = 1

Answer 8

do you understand how I came up with this now?

Answer 9

in regards to the formula I posted above?

Answer 10

Yes

Answer 11

Ok awesome,

\[\frac{y}{x} = \frac{a}{b}\]
\[\frac{y}{x}*\frac{x}{1} = \frac{a}{b}*\frac{x}{1}\]
\[\frac{y*x}{x*1} = \frac{a*x}{b*1}\]
\[\frac{y*x}{x} = \frac{a*x}{b}\]
\[y*1 = \frac{a*x}{b}\]
\[y = \frac{ax}{b}\]

this property works with division also, the denominator is 1 because you can express any number with a denominator 1 also I wanted to demonstrate basic fraction multiplication rule. Do the same with b, then multiply both sides of the equation by (1/a) and you will have solved for x

Answer 12

this is essentially how you will solve this problem remember a, b, y are all just numbers just like your problem

Answer 13

I'm confused again....I still don't know how to solve the problem.

Answer 14

\[\frac{378.24g}{x cm^3} = \frac{3.91g}{1cm^3}\]

Answer 15

does this make it easier?

Answer 16

you need solve for x to find the volume of 378.24grams of this material. First step you want to bring x up out of the denominator

Answer 17

so just multiply both sides by (x/1)

Answer 18

Yes that makes it easier, but I'm still confused on how to find out what x is. Would I divide 378.24g by 3.91 g to get 96.7 And that would be x?

Answer 19

just write it out like I did

Answer 20

above

Answer 21

on a piece of paper dont skip out on rules you wont make mistakes if you do, then when you feel comfortable skip them

Answer 22

one step at a time

Answer 23

What do you mean? I don't know how to solve for x.

Answer 24

your answer is right

Answer 25

So would I divide 378.24 by 96.7 and that would be my answer?

Answer 26

no, your answer is x

Answer 27

x is the volume you are looking for

Answer 28

So my answer is 96.7?

Answer 29

cm^3 is a volume

Answer 30

remember units!

378.24g/96.7cm^3 = 3.91 grams/1cm^3

Answer 31

do you understand now?

Answer 32

Yes I do.

Answer 33

also remember units cancel out when divided and they increase power when multiplied

cm*cm = cm^2

cm/cm = no units

cm^2/cm = cm

Answer 34

ok I'm gone hope this was insightful take care