A grocer mixes peanuts that cost $1.49 per pound and walnuts that cost $2.69 per pound to make 100 pounds of a mixture that costs $2.21 per pound. How much of each kind of nut did the grocer put into the mixture?

1.49x+2.69(100-x)=2.21*100

study that, then solve for x, the cheap nut

40 peanuts and 60 walnuts

To solve this problem, we can set up a system of equations based on the information given. Let's represent the amount of peanuts the grocer used as "x" pounds, and the amount of walnuts as "y" pounds.

1. The first equation represents the total weight of the mixture: x + y = 100 (since the grocer used 100 pounds in total).

2. The second equation represents the cost per pound of the mixture: (1.49 * x + 2.69 * y) / (x + y) = 2.21.

Now, we need to solve this system of equations. We can use the method of substitution:

1. Solve the first equation for x: x = 100 - y.

2. Substitute this value of x into the second equation:

(1.49 * (100 - y) + 2.69 * y) / (100 - y + y) = 2.21.

Simplifying the equation:

(149 - 1.49y + 2.69y) / 100 = 2.21.

Combine like terms:

(149 + 1.2y) / 100 = 2.21.

3. Multiply both sides of the equation by 100 to eliminate the denominator:

149 + 1.2y = 2.21 * 100.

Simplify:

149 + 1.2y = 221.

4. Subtract 149 from both sides:

1.2y = 221 - 149,

1.2y = 72.

5. Divide both sides by 1.2 to solve for y:

y = 72 / 1.2,

y = 60.

Now, we know that y (the amount of walnuts) is equal to 60 pounds. We can substitute this value back into the first equation to find the value of x (the amount of peanuts):

x + 60 = 100,

x = 100 - 60,

x = 40.

Therefore, the grocer put 40 pounds of peanuts and 60 pounds of walnuts into the mixture.

this sucks. you did not show the steps on how to solve it