application of equations

Question

A merchant has 5 pounds of mixed nuts that cost $30. he wants to add peanuts that cost $1.50 per pound and cashews that cost $4.50 per pound to obtain 50 pounds of a mixture that costs $2.90 per pound. how many pounds of peanuts are needed?

Answer 1

Multiply the number of pounds of each type and multiply by the cost per pound to get the total cost of that part contribution to the total. Add them together and set it equal to the final total pounds (50) multiplied by its cost per pound ($2.90) 

 

There are 5 pounds of mixed nuts.

let x = pounds of peanuts

45 - x = pounds of cashews

This way total pounds = 50

 

5 pounds($6/pound) + x pounds ($1.50/pound) + (45-x)pounds($4.50/pound) = 50 pounds($2.90/pound)

30 + 1.50x + 202.5 - 4.50x = 145

-3x = -87.5

x = 29.167

Answer 2

Shelly: Let the merchant add x pounds of peanuts. The total mixture is 50 pounds and he already has 5 pounds of mixed nuts. So he MUST have 50 - 5 - x pounds of cashews only. The cost of the 50 pounds mixture is (50)(2.90) = $145. The equation is 30 + (1.5) x + (50 - 5 -x)(4.5) = 145. 30 + 1.5 x + 225 - 22.5 - 4.5 x = 145 255 - 22.5 - 145 = 3 x 110 - 22.5 = 3 x 77.5 = 3 x x = 25.83 pounds (to 2 decimals). Please check my arithmetic. Dr. G.

Answer 3

You will need to write two equations--one for the total price and one for the total amount of nuts.  Let x = the number of pounds of peanuts and y = the number of pounds of cashews.

 

50 = 5 + x +y for the total amount of nuts.

 

(2.90)(50)  = 30 + 1.50x + 4.50y for the total cost.

 

 

Solve for x and y.

Answer 4

Say, peanuts = x lbs

  cashews = y labs

 

Total peanuts and cashews added = 45 lbs

 

x+y = 45.           equation no 1

 

Final mixture cost = 2.9 $/lbs  total mixture = 50 labs

 

Total mixture cost=2.9*50=145 $

Cost od peanut and cashews added =145-30=115 $

 

So,

1.5x+4.5y=115

3x. + 9y   =230.  equation no 2

 

Solving 1 & 2

 

x=29.17 lbs

y=15.83. lbs 

 

So peanuts=29.17 lbs

    cashews = 15.83 lbs