a store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. the manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. how many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Question

a store sells cashews for $5.00 per pound and peanuts for $1.50 per pound. the manager decides to mix 30 pounds of peanuts with some cashews and sell the mixture for $3.00 per pound. how many pounds of cashews should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts separately?

Answer 1

Equate total selling price of mixture to total selling price of components. Solve for weight of cashews.

Let
x=weight of cashews to be added
Total price of mixture
= 3(30+x)
Total price of components
= 30*1.5 + 5x

Equate and solve for x:
3(30+x) = 30*1.5 + 5x
Isolate x and solv
5x-3x = 3(30)-30(1.5)
2x = 45
x = 22.5 lbs

Answer 2

thanks a million!

Answer 3

The grocery store sells kumquats for $3.75 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weights of kumquats k and Asian pears p that a customer could buy with $14.

Answer 4

To find out how many pounds of cashews should be mixed with the peanuts, we need to determine the ratio between the prices of the two types of nuts.

Let's assume we need to mix "x" pounds of cashews with the 30 pounds of peanuts. Since the manager decides to sell the mixture for $3.00 per pound, the revenue obtained from selling the mixture will be equal to the revenue obtained from selling the cashews and peanuts separately.

The revenue from selling the peanuts alone can be calculated by multiplying the price ($1.50) by the weight (30 pounds): $1.50 * 30 = $<<1.50*30=45.00>>45.00.

Now, let's calculate the revenue from selling the mixture. The average price per pound of the mixture is $3.00, and the total weight of the mixture is (30 + x) pounds. Therefore, the revenue from selling the mixture is $3.00 * (30 + x).

Since the revenue from selling the mixture should be equal to the revenue from selling the peanuts alone, we have the equation:

$3.00 * (30 + x) = $45.00

Now, we can solve this equation to find the value of x:

3 * (30 + x) = 45
90 + 3x = 45
3x = 45 - 90
3x = -45
x = -45 / 3
x = -15

Since x represents the pounds of cashews, it cannot be a negative value. Therefore, it is not possible to mix a negative weight of cashews with the peanuts to produce the same revenue as selling them separately.

Hence, it is not possible to mix any pounds of cashews with the peanuts in such a way that the mixture will produce the same revenue as selling the nuts separately.