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.

Question

1. Solving Systems of Equations
2. Using Elimination

Answer 1

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

You can check by plugging the values into the equations 1 and 2.

I hope you find this useful if you have any questions send me a message.

Answer 2

assume that 1pound cashew cost is x dollar and 1 pound peanut cost is y dollar

in case of rosa she bought 1pound cahsew and 2 pound peanut and cost 10 dollar

so, x+2y=10 -------1

and sabrina bought 2 pound cashew and 1 pound peanut

so, 2x+y=11---------------2

solving 1 & 2 equation

we get x= 4 dollar

and y= 3 dollar

solution

x+2y= 10

2x+y=11

multiply equation 1 by 2 we get

2x+4y=20

and now

2x+4y=20

2x+y=11

------------

so x=4

and y=3