Question

Rosa bought 1 pound of cashews and 2 pounds of peanuts for $10. At the same store, Sabrina bought 2 pounds of cashews and 1 pound of peanuts for $11. Find the cost per pound for cashews and peanuts.
- Solving Systems of Equations ( word problem)
- Using Elimination

Answer 1

Answer: Cashews are $4 per pound

Peanuts are $3 per pound

Explanation

Let x = Cashews

Let y = Peanuts

Given the information above

Rosa's purchase is equation number 1

x + 2y = 10

Sabrina's purchase is equation number 2

2x + y = 11

We have

Equation 1  x + 2y = 10

Equation 2  2x + y = 11

If we multiply equation 1 by negative 2 we can eliminate x and solve for y as follows:

-2(x + 2y = 10) gives

-2x - 4y = -20

Combine this with the equation 2

-2x - 4y = -20

2x + y = 11

The x is eliminated and we get

-3y = -9

Divide both sides by - 3 to solve for y and we get

y = 3

We substitute this value for y back into equation 2 to solve for x

2x + 3 = 11

2x = 11 - 3

2x = 8

Divide both sides by 2 to solve x we have

x = 4

Cashews are $4 per pound

Peanuts are $3 per pound

I hope that this will help you.