Question

A nut store normally sells cashews for? $4.00 per pound and peanuts for? $1.50 per pound. But at the end of the month the peanuts had not sold? well, so, in order to sell 40 pounds of? peanuts, the manager decided to mix the 40 pounds of peanuts with some cashews and sell the mixture for $2.00 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in the? profit?

Answer 1

Answer:

  10 lbs

Step-by-step explanation:

Let c represent the number of pounds of cashews to be added. Then the total cost of the mix will be ...

  4.00c +1.5(40) = 2.00(c+40)

  4c +60 = 2c +80 . . . . . . . . . . . simplify

  2c = 20 . . . . . . . . . . . . . . . . . . . subtract 60 + 2c

  c = 10 . . . . . . . . . . . . . . . . . . . . .divide by 2

10 pounds of cashews should be mixed with the peanuts.

Answer 2

The mixture of cashew and peanut is an illustration of a linear equation. The pounds of cashew that would ensure no change in the profit is 20 pounds

Represent the cashew with c, and the peanuts with p.

So, we have:

$U_c =4.00$ --- the unit selling price of cashew

$U_p = 1.50$ --- the unit selling price of peanuts

$U_m = 2.00$ --- the unit selling price of the mixture

$p =40$ ---- the pounds of peanuts that has not been sold.

$m = 40 + c$ --- the mixture when the 40 pounds of peanut is mixed with cashew.

The equation to solve for c is:

$U_c \times c +U_p \times p =U_m \times m$

This gives:

$4.00 \times c +1.50 \times 40 = 2.00 \times (40 + c)$

$4c +60 = 80 + 2c$

Collect like terms

$4c - 2c = 80 -60$

$2c = 20$

Divide both sides by 2

$c = 10$

Hence, 20 pounds of cashew would ensure no change in the profit.

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