Question

HELP THIS WORD PROBLEM SEEMS EASIER THAN YOU THINK. A dish of nuts contains cashews and peanuts. 2 more ounces of peanuts are added to the dish, making the new mixture 20% cashews. 2 more ounces of cashews are added, making the dish 33 1/3 % cashews. What percent of the original mixture of nuts was cashews?

Answer 1

you have to know how many ounces of nuts are in the dish to begin with to solve the problem

Answer 2

you have added the same ratio of pnuts and cashews so their ratio remains the same ...

Answer 3

meaning...?

Answer 4

if things remain the same ,,, then what does that tell us about the start and ending values?

Answer 5

Then the start and end values would be of the same ratio to the other percents

Answer 6

Amistre64 is incorrect, the ratio doesn't necessarily remain the same

Answer 7

it would only remain the same if the starting ratio is 1:1

Answer 8

are we assuming count or weight?

Answer 9

do you know how to setup a system of equations?

Answer 10

the only thing we have to go on is weight

Answer 11

im open to being mistaken :)

Answer 12

so am I :) so excuse me if I'm incorrect but I believe to solve this you need to setup a basic system of equations by modeling the two parts of the problem. Btw since this is my first time doing this, how much help should we give?

Answer 13

hmm, guide, but let the asker participate. and correct as needed.

Answer 14

Ahhh thank you! So Vincent, do you have an idea of how to do this problem?

Answer 15

The dish started with p ounces of peanuts and c ounces of cashews.
The original ratio is p/c and is unknown.
Then 2 ounces of peanuts are added.
Now the ratio is: (p + 2)/c = 4/1
Then, 2 ounces of cashews are added.
The new ratio is (p + 2)/(c + 2) = 2/1

Answer 16

Well... Not really. Ratios with different units confuse me a lot

Answer 17

Solve the system of equations:
\(\dfrac{p+2}{c} = 4\)
\(\dfrac{p+2}{c+2} = 2\)

Answer 18

so solve for c? Since we're looking for the cashew percent?

Answer 19

mathstudent your equations are incorrect and not that helpful if he doesn't understand what he is doing.

Answer 20

Find p and c, then find what percent of the total c is.

Answer 21

1DEA, how's mathstudent55 incorrect?

Answer 22

Oh wait actually they are right but do you understand how he is modeling those equations?

Answer 23

Yea. Ratios of the cashews and ounces. I just solved both... C = 2

Answer 24

If you don't understand how I arrived at the equations, read my explanation above.

Answer 25

ok cool that's good if you understand how to do it, as it is more important to be able to arrive at those equations than just simply being able to solve the equations

Answer 26

i was considering the rations as


c
--- = original percentage of c to (c+p)
c+p


c
------ = .2
c+p+2


c+2
----- = .3333
c+p+4

Answer 27

@mathstudent55, I briefly glanced at it initially and was confused for a sec.

Answer 28

mathstudent, so if c= 2 , there was originally 2 ounces of cashews??

Answer 29

@1DEA No problem.

Answer 30

@amistre64 that's completely correct

Answer 31

Yes, there were originally 2 ounces of cashews.
Now you need the original number of ounces of peanuts.

Answer 32

there were 6 ounces of peanuts

Answer 33

so if there were 8 ounces in total... I just need to find 2 percent out of 8??

Answer 34

yes

Answer 35

2 is what percent of 8?

Answer 36

25%

Answer 37

correct

Answer 38

Awesome. Thanks all of you!

Answer 39

yw

Answer 40

np