How would you do this problem?

Question

Cashews sell for $1.20 per quarter-pound,and brazil nuts sell for $1.50 per quarter-pound.How many pounds of cashews should be mixed with 20 pounds of brazil nuts to get a mix that sells for $1.30 per quarter-pound?


Thank you! I have no idea how to do this stuff

Answer 1

1.20x+20(1.50)=(x+20)(1.30)
1.20x+30=1.30x+26
0.10x=4
x=40 so 10 pounds of cashew should be added

Answer 2

We should mix 40 pounds of cashews with the 20 pounds of brazil nuts to get a mix that sells for $1.3 per quarter-pound .
It solved as followes:
let the weight of cashews needed be x
the price of one pound of cashews = 1.2*4=$4.8
and the brazil nuts =1.5*4=$ 6
the price of one pound of the mix =1.3*4=$5.2
So our mix price will be ((20*6)+(x*4.8))/(20+x)=$5.2
120+4.8x=104+5.2x
solving for x=16/.4=40 pound
so 20 pound of brazil nut =$120
and 40 pound of cashews=40*4.8=$192
the total weight is 60 pounds
$120+192=$312
312/60=5.2
5.2/4=1.3

Answer 3

It can be written as:

(20(4) * 1.5 + 1.2 * 4 * x) / (80 + 4x) = 1.3

Which means 20 pounds of brazil nuts times the price of brazil nuts plus x pounds of cashews times the price of cashews all divided by the total amount of nuts in quarter pounds.

Simplify and you get:

(120 + 4.8x) / (80 + 4x) = 1.3

120 + 4.8x = 104 + 5.2x

.4x = 16

x = 40

You need 40 lbs of cashews!

Answer 4

What we want to do is write an equation which gives the price per quarter pound as a function of pounds of cashews, set that equation equal to $1.30, and solve for x.

Price per quarter pound = (4.8x +6 * 20)/(4(x+20))
The numerator is the total price of the mix, the denominator is the number of quarter pounds.

1.3 = (4.8x+120)/(4x+80)
5.2x+104=4.8x+120
.4x=16
x=40 lbs of cashews

Answer 5

You start it by saying that we know we have 20 pounds of brazil nuts at 1.50/pound, and we need c pounds of cashews at 1.20 a pound. We want the mixture to total 1.30/pound
We set up the equation as such:
20(1.50) + c(1.20) = 1.30 (20 + c)
Now, solving it, we get:
30 + 1.2c = 26 + 1.3c
.1c=4
so c = 40.
So we need 40 pounds of cashews.
If you have any questions about the set-up, feel free to ask... :-)

Answer 6

This is a type of problem known as a value problem.
The setup works as follows:
value of cashews + value of brazil nuts = value of total mix.
So let x be the number of cashews.
Then
1.2x + 1.5(20) = 1.3(x + 20),
since there are x + 20 nuts in the total mix.
Thus
1.2x + 30 = 1.3x + 26
0.1x = 4
x = 40
check: 1.2(40) + 1.5(20) = 1.3(40 + 20).
Most value problems can be set up this way.

Answer 7

Thinking.............40lbs