Question

Mixture problems confuse me. Can someone show me how to solve this so I can know what to do for future reference?

A health food store sells oatmeal for $3.60 per pound and bran flakes for $4.80 per pound. How many pounds of each should be used to get a mixture of 30 pounds that sells for $4.00 a pound?

A. 15 lbs oatmeal, 15 lbs bran flakes
B. 20 lbs oatmeal, 10 lbs bran flakes
C. 15 lbs bran flakes, 15 lbs oatmeal
D. 20 lbs bran flakes, 10 lbs oatmeal

Answer 1

ok, I think I can help you here.

Answer 2

firstly, it always helps to use symbols to represent the unknowns when solving questions like this.

Answer 3

so, lets say the mixture contains 'x' pounds of oatmeal and 'y' pounds of bran flakes

Answer 4

then we know the total cost of the mixture will be:\[x*3.60+y*4.80\]

Answer 5

we are also told that the total weight of the mixture is 30 pounds, so we know:\[x+y=30\]

Answer 6

do you understand so far?

Answer 7

yes , ^_^

Answer 8

ok, good, now we are told the mixture is "30 pounds that sells for $4.00 a pound"

Answer 9

so what do you think will be the total cost of the mixture?

Answer 10

4 * 30

Answer 11

$120 ?

Answer 12

120?

Answer 13

@lilg132 - you should let @Cj Sade answer so that she can learn.
@Cj Sade - correct

Answer 14

sorry

Answer 15

ok, now earlier in the steps, we showed that the total cost of the mixture was:\[x*3.60+y*4.80\]so now we can write:\[x*3.60+y*4.80=120\]

@lilg132 - no worries - I am just trying to help @Cj Sade understand.

Answer 16

Its ok : )

Answer 17

so we now have two equations in two unknowns:\[x+y=30\]\[3.6x+4.8y=120\]

Answer 18

if you are uncomfortable with decimals, then you can just multiply the 2nd equation by 10 to get:\[36x+48y=1200\]then divide both sides by 12 to get:\[3x+4y=100\]

Answer 19

so we finally end up with:\[x+y=30\]\[3x+4y=100\]do you know how to solve this?

Answer 20

Ummm , no not really .Walk me through it ?

Answer 21

ok

Answer 22

this type of problem is called "simultaneous equations" - but that is not important right now.

so, we ended up with:\[x+y=30\]\[3x+4y=100\]use the first equation to get an expression for 'y' so that we can substitute it into the 2nd equation.
so, from the 1st equation, we get:\[y=30-x\]substituting this into the 2nd equation gives:\[3x+4(30-x)=100\]\[3x+120-4x=100\]\[120-x=100\]so:\[x=120-100=20\]

Answer 23

use this to work out what y is as we know \(y=30-x=30-20=10\)

Answer 24

did you understand those steps?

Answer 25

yes , one second .

Answer 26

its ok - take your time... it's important that you understand how this was done.

Answer 27

is there a particular step that is still confusing you?

Answer 28

Ok I just reviewed everything you said and I think I got the hang of it , Im gonna go try out some practice problems just to be sure, but thankyou so much : )

Answer 29

what answer did you get cj sade?

Answer 30

I got answer B, is that correct?

Answer 31

yes

Answer 32

Yaaay :D Thanks guys .

Answer 33

your welcome even though it was asaneer who explained brilliantly :p

Answer 34

Yes , Thankyou asnaseer :)

Answer 35

@lilg132 ^ LOL!
@Cj Sade you are more than welcome - I'm glad I was able to explain it to you.