Question

General purpose concrete is created using a 1:2:3 ratio of cement to sand to gravel. If we have 150 kgs of sand available, how many kgs of concrete can we make? (Assume we have more than enough cement, and gravel.)

Answer 1

how have you tackled this problem thus far?

Answer 2

havin a hard time

Answer 3

tryna figure out a way to do it without proportions

Answer 4

hmmm why so?

Answer 5

cuz i hate proportions

Answer 6

mmm I see well unfortunately this problem screams proportions but it's really not that bad! Can we please use proportions???

Answer 7

fine but u have to explain proportions first

Answer 8

ok I will try my best! So we are making concrete made up of 1 part cement, 2 parts sand, and 3 parts gravel. And we have 150kgs of sand and want to know how much concrete we can make. So our first step would be thinking about how much cement and gravel to add to make the concrete correct?

Answer 9

why is it \[\frac{ 1 }{ 3 } = \frac{ 150 }{ x }\] how come 150 goes on top?

Answer 10

well tell me what does x represent?

Answer 11

kgs of concrete

Answer 12

so what you are saying is that the proportion of the weight of the sand(given by the 150) is 1/3 of the total. Does that make sense?

Answer 13

hmmmm a little bit

Answer 14

well that's just what the equation you gave me means correct? Which btw I am still puzzled as to how you came to that. Mind explaining it to me?

Answer 15

its the answer

Answer 16

i dont want the asnwer tho i wanna know how to do it

Answer 17

yes it is! haha so I am guessing you looked it up?

Answer 18

I concur that's a good thing!

Answer 19

well let me explain how to get there. So we have the ratio of 1(cement):2(sand):3(gravel) right? Can you see that the sand is 1/3 of the total from this? (kinda hard right?)

Answer 20

yea

Answer 21

show me how

Answer 22

i get how i got 1/3 i just dont understand why the 150 is on top instead of the denominator

Answer 23

u add all them up and then you make it sand/total which is 2/6 = 1/3

Answer 24

nice alright! Well let ignore the math for a sec and just think: if 1/3 of the total weighs 150kg, what does the total weigh?

Answer 25

50?

Answer 26

hmmm what if we knew that a half of something weighed 150 what would the whole thing weigh?

Answer 27

300

Answer 28

so if we know that a third of something weighs 150 what would the whole thing weigh?

Answer 29

450?

Answer 30

RIGHT!

Answer 31

so let's go back to the Math now you asked why the 150 is on top right?

Answer 32

hmmmm so in other instances if it was like 1/7 i can multiply it by 7?

Answer 33

exactly!

Answer 34

makes sense in english right?

Answer 35

what if it was like 2/7

Answer 36

well let's take that apart: 2/7 is like 2 times 1/7 so... you would...?

Answer 37

?

Answer 38

haha. Let's see. If I know that two of something weighs 50 the total would be?

Answer 39

sorry not total I mean one of something

Answer 40

hmmmm not too sure

Answer 41

well if 2 of something weighs 50, 1 of the same thing would be simply 25 right?

Answer 42

yea gotcha

Answer 43

25 x 2 = 50

Answer 44

so you basically do the inverse to get the original thing right? so for 2/7 you would simply do the inverse aka 7/2.

Answer 45

and then multiply?

Answer 46

yup so if we know that 2/7 of something weighs 100, what would the entire thing weigh?

Answer 47

7/2 x 100?

Answer 48

yeah! now let's go to the math because that's unfortunately how we have to solve most of our math problems in. So you asked why the 150 was on top right? Do you understand why now?

Answer 49

i think so hey can you use the same method if 150 was on the bottom? or any other number for that matter?

Answer 50

hmmm well what would it mean if 150 was on the bottom?

Answer 51

its the whole

Answer 52

right and yup as long as you know that that's its particular proportion.

Answer 53

so are you understanding proportions a little better now?

Answer 54

so if its 2/7 = x/150 i would multiply without inversing anything right? so 2/1050

Answer 55

Hmm no, I can see how the math is hard to understand. Here's another way to look at this (and really the way I look at it). What we really want to do is solve for x right? And that means getting x by itself. So how would we do it?

Answer 56

by isolating it and moving numbers to the opposite side

Answer 57

yup and when you do that?

Answer 58

u multiply 150 by 2 and divide by 7

Answer 59

so you wouldn't get 2/1050, does that make sense? or have I lost you?

Answer 60

naw i think i got it now

Answer 61

alright nice! Do you have any other problems?

Answer 62

On a certain high school team, the ratio of sophomores to juniors is 2:3, and ratio of juniors to seniors is 5:6. Sophomores are what fraction of the whole team?

Answer 63

well how would start tackling this problem? Btw what grade/math level is this for?

Answer 64

honestly im really bad at math and I'm studying for the GRE to get into a Phd program

Answer 65

ahhh that's cool I am in a Master's program myself (though I am currently just slacking off lol). But that's totally unrelated lol so how would you start this problem?

Answer 66

um i have no clue since it has 2 ratios

Answer 67

what should i do

Answer 68

so there's really two ways of doing this problem: what I call the example method and the mathematical way. Which would you like to hear about?

Answer 69

whichever is easier and fastest

Answer 70

normally id like to hear both but i really have to sleep to get up earl for math tutoring so yea the simple method please

Answer 71

well the simpler method is also the more specific method, simply put you can just put in numbers to this problem.
So if you have a Sophomore: Junior ratio of 2:3 and a Junior:Senior of 5:6
you can just say that you have...let's say you have idk 10 sophomores that means you have
how many juniors?

Answer 72

15

Answer 73

and if you have 15 juniors how many seniors do you have?

Answer 74

30

Answer 75

wait no

Answer 76

how did you get 30?

Answer 77

5*6

Answer 78

how did you get how many juniors previously?

Answer 79

5*3

Answer 80

where did you get the 5 from? (it's correct but how)

Answer 81

divided by the 10 u gave

Answer 82

so you did 10 /2 * 3 right?

Answer 83

yes

Answer 84

so why not do the same thing for the junior:senior ratio? So with a ratio of 5:6 and 15 juniors, how many seniors?

Answer 85

11/ 5?

Answer 86

no so you have 15 juniors so you would divide by 5 and then multiply by 6 right? Or are you lost?

Answer 87

what r u multiplying by 6?

Answer 88

because that the ratio of seniors

Answer 89

no, what are you multiplying not why

Answer 90

Here let me back up because that's kinda hard to explain. So we have a ratio of 5:6 j:s so for every 5 juniors we have 6 seniors. Since we know that we have 15 juniors we must have 18 seniors since 15/5*6 =18.

Answer 91

why did u divide 15 by 5?

Answer 92

well let's think about it. So for every 5 juniors we have 6 seniors and if we have 15 juniors how many seniors would we have?

Answer 93

18

Answer 94

so do you see why I divided 15 by 5?

Answer 95

no...

Answer 96

I wanted to see how many groups of 5 I had because for every group of 5 juniors I have 6 seniors

Answer 97

oh okay

Answer 98

so how many seniors do we have?