need help with another math word problem!!?

Question

A nut store usually sells cashews for $4.50 per pound and peanuts for $1.90 per pound. At the end of the month, the peanuts had not sold well. In order to sell 50 pounds of peanuts, the manager decided to mix the 50 pounds of peanuts with some cashews and sell the mixture for $2.50 per pound. How many pounds of cashews should be mixed with the peanuts to ensure no change in profit? (The vaule remains the same)

Answer 1

cashews: $4.50 / lb
peanuts: $1.90 / lb
mixed at $2.50/ lb
Let 50 lb peanuts be mixed with x lb of cashews

sale price = 1.90(50) + 4.50 x
# of lb = 50 + x @ $2.50/lb
total = (50 + x)(2.5)

(50 + x)2.5 = 1.90(50) + 4.5x
125 + 2.5x = 95 + 4.5x
(4.5 - 2.5)x = 125 - 95
2.0x = 30
x = 15
He needs to mix with 15 lb cashews

Answer 2

Let x be the quantities of cashews added.

50 pounds of peanuts cost 50 x 1.90 = 95 dollars

x pounds of cashews cost x multiplied by 4.50 = 4.5 x dollars

Amount realised by selling the mixture = 2.50 (50 + x) = 125 + 2.5x

We can write 125 + 2.5x = 95 + 4.5x

Taking the x terms to one side,

30 = 2x

x = 15

So, he can add 15 pounds of cashew and realise a mixture of 65 pounds, which will fetch him 162.50 dollars. The profit remains same.

Answer 3

in a nutshell the answer is 15 pounds of cashews

x = lbs of cashews to satisfy the condition

[ 50 (1.9) + x (4.5) ] / (50+x) = 2.5

Answer 4

x= pounds of cashews
50*1.9 +4.5x =2.5(x+50)
95 +4.5x =2.5x +125
2x = 30
x = 15 pounds