Wild rice sells for $6 pound, and plain rice sells for $1 per pound. A grocer wants 10 pounds if the mixture to sell for $2 per pound. How much of each type should he used?

Question

Wild rice sells for $6 pound, and plain rice sells for $1 per pound. A grocer wants 10 pounds if the mixture to sell for $2 per pound. How much of each type should he used?

Answer 1

wild rice needed --- x lbs

plain rice needed -- 10-x lbs

6x + 1(10-x) = 2(10)
6x + 10-x = 20
5x = 10
x = 2

he needs 2 lbs of wild rice and 8 lbs of plain rice

Answer 2

Let's assume the grocer uses x pounds of wild rice and y pounds of plain rice.

The total weight of the mixture is x + y pounds.

The cost of the wild rice is $6 per pound, so the cost of x pounds of wild rice is 6x dollars.

The cost of the plain rice is $1 per pound, so the cost of y pounds of plain rice is y dollars.

The total cost of the mixture is 6x + y dollars.

The mixture should sell for $2 per pound, and the total weight of the mixture is x + y pounds. So, the total cost of the mixture should be (x + y) * 2 dollars.

Since the grocer wants the cost of the mixture to be $2 per pound, we can set up the equation:

6x + y = (x + y) * 2

Simplifying the equation:

6x + y = 2x + 2y

Rearranging the terms:

6x - 2x = 2y - y

4x = y

So, y = 4x.

Since the grocer wants 10 pounds of the mixture, we can set up another equation for the total weight:

x + y = 10

Substituting y = 4x:

x + 4x = 10

5x = 10

x = 10 / 5

x = 2

So, the grocer should use 2 pounds of wild rice.

Substituting x = 2 in y = 4x:

y = 4 * 2

y = 8

So, the grocer should use 2 pounds of wild rice and 8 pounds of plain rice.

Answer 3

To determine how much of each type of rice the grocer should use, we can set up a system of equations based on the given information.

Let's assume the grocer uses 'x' pounds of wild rice and 'y' pounds of plain rice:

1) The total weight of the mixture is 10 pounds, so we have the equation:
x + y = 10

2) The grocer wants the mixture to sell for $2 per pound, so the total cost of the mixture can be expressed as:
6x + 1y = 2 * 10

Now, we have a system of two equations:
1) x + y = 10
2) 6x + y = 20

We can solve this system of equations using the method of substitution or elimination.

Using the substitution method:
From equation 1, we can express x in terms of y by subtracting y from both sides:
x = 10 - y

Substituting this value of x into equation 2:
6(10 - y) + y = 20
60 - 6y + y = 20
-5y = 20 - 60
-5y = -40
y = (-40) / (-5)
y = 8

Now, substitute the value of y into equation 1 to find x:
x + 8 = 10
x = 2

Therefore, the grocer should use 2 pounds of wild rice and 8 pounds of plain rice to achieve the desired mixture.