If you get mixed nuts with cashews that cost $6.25 lb. and if you get mixed nuts with peanuts @ $2.30 lb. But if I just want 1/2 lb. of mixed nuts for $1.70 how much of each would be included?

x with cashews costs 6.25 x

(.5-x) with peanuts costs 2.30 (.5-x)
so
6.25 x + 2.30(.5-x) = 1.70

How many lbs of cashew and how many of lbs.peanuts

is it 0.139 of the cashews

3.95 x + 1.15 = 1.70

3.95 x = .55

x = .139 yes
then .5 - x = .361
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check
6.25 * .139 = .869
2.30 * .361 = .830
------------------- add
****** .5 lbs = 1.699 or in other words 1.70

To solve this problem, we will set up a system of equations. Let's define the variables:

- Let's call the weight of cashews as "c" (in pounds).
- Let's call the weight of peanuts as "p" (in pounds).

Now, let's set up the equations based on the given information:
1. We know that the cost of 1 pound of cashews is $6.25. Therefore, the cost of "c" pounds of cashews is 6.25c.
2. We also know that the cost of 1 pound of peanuts is $2.30. Therefore, the cost of "p" pounds of peanuts is 2.30p.
3. The mixed nuts available for $1.70 are 1/2 pound. Therefore, the cost of 1/2 pound of mixed nuts is $1.70.

From these equations, we can set up the following equations:
6.25c + 2.30p = 1.70 (equation 1)
c + p = 1/2 (equation 2)

Now, we can solve the system of equations to find the values of "c" and "p".

First, let's isolate "c" in equation 2:
c = 1/2 - p (equation 3)

Now substitute equation 3 into equation 1:
6.25(1/2 - p) + 2.30p = 1.70
Simplify the equation:
3.125 - 6.25p + 2.30p = 1.70
Combine like terms:
-3.95p = -1.425
Divide both sides by -3.95:
p = -1.425 / -3.95
p ≈ 0.36

Now substitute the value of "p" back into equation 3 to find the value of "c":
c = 1/2 - 0.36
c ≈ 0.14

Therefore, approximately 0.14 pounds (or 2.24 ounces) of cashews and approximately 0.36 pounds (or 5.76 ounces) of peanuts would be included if you want 1/2 pound of mixed nuts for $1.70.