Confusing Problem

Question

Hello! If some could post a step-by-step solution to this problem that would be super helpful because I am confused as to how to set this up. 

 

Problem: A coffee company wants a new flavor of Cajun coffee. How many pounds of coffee worth $8 a pound should be added to 10 pounds of coffee worth $5 a pound to get a mixture worth $6 a pound? 

 

 

 

Answer 1

Hi Karen,

 

Imagine two piles of coffee. One contains 10 pounds and each pound is worth $5. So that pile is worth $50.

 

The second pile we do not know the number of pounds so let's call that x. That pile is worth $8 for each pound. If we multiply x by 8 we will have the worth of the second pile, that is 8x.

 

Now we dump the second pile onto the first file. How many pounds to we have on the combined pile? (x + 10). We want the combined pile to be worth $6 for each pound. So the worth of the combined pile is 6 (x + 10).

 

The worth of the combined pile is also equal to the worth of the separate piles added together which can be represented by 8x + 50. We want that value to be equal to 6(x+10).

 

This is the equation you want to set up and solve (where x represents the # pounds of $8 coffee).

 

8x + 50 = 6 (x + 10)

 

You should be able to take it from there.

Answer 2

x represents the amount added

 

$5(10) + $8x = $6(10 + x)

50 + 8x = 60 + 6x

50 + 2x = 60

2x = 10

x = 5