if a man mixes 12 lbs. of peanuts that's $1.25 a lbs. with a pound of cashews at $1.80 a lbs. how many pounds of cashew do you need to make a $1.50 a lbs. mixture

explain in words and numbers

To find the pounds of cashews needed to make a $1.50 per pound mixture, we need to set up an equation using the weighted average formula.

Let's assume we need "x" pounds of cashews.

The total weight of the mixture will be 12 + x pounds.

The cost of the peanuts is $1.25 per pound, and since 12 pounds are used, the cost of the peanuts in the mixture is 12 * $1.25 = $15.

The cost of the cashews is $1.80 per pound, and since "x" pounds are used, the cost of the cashews in the mixture is x * $1.80 = $1.80x.

Now, let's set up the equation to find the pounds of cashews needed:

Total cost of the mixture = Cost of peanuts + Cost of cashews

$1.50 * (12 + x) = $15 + $1.80x

Now, we solve the equation to find the value of "x".

$1.50 * 12 + $1.50 * x = $15 + $1.80x

18 + $1.50x = $15 + $1.80x

Rearranging the equation, we get:

$1.80x - $1.50x = $18 - $15

$0.30x = $3

Dividing both sides of the equation by $0.30, we get:

x = $3 / $0.30

x = 10

Therefore, 10 pounds of cashews should be mixed with 12 pounds of peanuts to make a $1.50 per pound mixture.

To solve this problem, we can use a basic formula:

(weight of peanuts * price of peanuts) + (weight of cashews * price of cashews) = (weight of mixture * price of mixture)

Let's denote the weight of cashews needed to make the mixture as 'x' pounds. We know the following information:

Weight of peanuts = 12 lbs.
Price of peanuts = $1.25 per pound
Weight of cashews = 1 lb.
Price of cashews = $1.80 per pound
Price of mixture = $1.50 per pound

Using the formula, we can set up the equation:

(12 * 1.25) + (1 * 1.80) = (12 + x) * 1.50

Now, let's calculate:

15 + 1.8 = (12 + x) * 1.5

16.8 = (12 + x) * 1.5

Divide both sides by 1.5 to isolate (12 + x):

16.8 / 1.5 = 12 + x

11.2 = 12 + x

Subtract 12 from both sides:

11.2 - 12 = x

-0.8 = x

The weight of cashews needed to make a $1.50 per pound mixture is -0.8 pounds. However, a negative weight does not make sense in this context. Therefore, it is not possible to make a $1.50 per pound mixture with the given peanuts and cashews.