Colombian coffee beans cost $5.50/lb while Peruvian coffee beans cost $4.25/lb. We want to mix the beans together so as to produce a 40 lb bag costing $4.60/ lb. How many pounds of each type of beans shouold be used ?

Please help and show work

amount of Columbian stuff --- x lbs

amount of Peruvian stuff ----- 40-x lbs

5.5x + 4.25(40-x) = 4.6(40)

solve for x

To solve this problem, we need to set up a system of equations based on the information given.

Let's assume x represents the weight in pounds of Colombian coffee beans and y represents the weight in pounds of Peruvian coffee beans.

1. The first equation represents the total cost of the 40 lb bag:
5.50x + 4.25y = 4.60 * 40

2. The second equation represents the total weight of the 40 lb bag:
x + y = 40

We can solve this system of equations using either substitution or elimination. Let's use the elimination method.

Multiply equation 2 by 5.50 to make the x coefficients equal:

5.50(x + y) = 5.50 * 40
5.50x + 5.50y = 220

Now we have the system of equations:

5.50x + 4.25y = 4.60 * 40
5.50x + 5.50y = 220

By subtracting the equations from each other, we can eliminate the x variable:

5.50x - 5.50x + 4.25y - 5.50y = 4.60 * 40 - 220
-1.25y = -36

Divide both sides of the equation by -1.25 to solve for y:

y = -36 / -1.25
y = 28.8

Now substitute the value of y back into equation 2 to solve for x:

x + 28.8 = 40
x = 40 - 28.8
x = 11.2

So, you should use 11.2 pounds of Colombian coffee beans and 28.8 pounds of Peruvian coffee beans in order to produce a 40 lb bag costing $4.60/lb.

Please note that it is not possible to have fractional weights, so in practical terms, you could use 11 pounds of Colombian coffee beans and 29 pounds of Peruvian coffee beans to achieve a similar result.