If Cashews are 15 per kg and pecans are 10 per kg How many kilograms of each should be mixed in order to get 20kg of mixture worth 12 per kg?

Answer 1

Hello, we need to use two equations: 1st equation. c + p = 20 where c = weight of cashews to include, in kgs., and p = weight of peanuts to include, in kgs. Note that we need to end up with 20 kg total mixture, which is why c + p = 20. 2nd equation. 15c + 10p = 20 * 12, or simplified: 15c + 10p = 240 We get this 2nd equation since we know that $15 multiplied by the weight of the cashews plus $10 multiplied by the weight of the peanuts needs to total up to $240 (derived from 20 kg at $12 per kg) which is the desired total value of the 20 kg mix. The solution. To solve the two equations, we proceed as follows: c + p = 20 (this is the first equation) c + p - p = 20 - p (subtract p from both sides of equation) c = 20 - p (see how this equation is still equal to the original version?) Now, the trick to solving the problem is to substitute the value which we found for "c" by manipulating the first equation into the second equation where we see "p". Recall, here is the 2nd equation: 15c + 10p = 240 So now we substitute in "20 - p" for c since we determined above that c = 20 - p: 15(20 - p) + 10p = 240 (see how this is still equal to the original equation 2) Notice that this is easy to start to solve since it only has one variable; we eliminated c from it: 300 - 15p + 10p = 240 (we just multiplied out the 15(20 - p) value) -15p + 10p +300 = 240 (I just reordered the left hand side to make it clearer) -15p + 10p + 300 - 300 = 240 - 300 (subtract 300 from both sides) -15p + 10p = -60 (this is what we get after doing that subtraction) -5p = -60 (we just combined the two values on the left hand side) 5p = 60 (multiplied both sides by -1) p = 12 (divided both sides by 5) So now we know one of our values, p=12. That means that the mix will have 12 kg of peanuts. So how many cashews? Simple, let's go back to our first equation: c + p = 20 (remember this means weight of cashews + weight of peanuts = 20 kg total). so now we know that p=12, substitute that in to the first equation: c + 12 = 20 c = 20 - 12 c = 8 So now we have the second part of the solution: 8 kg. of cashews. So the entire solution is: 8 kg of cashews and 12 kg of peanuts (this is the answer) Finally let's check the answer... (8 * 15) + (12 * 10) =? 240 120 + 120 =? 240 240 =? 240 Yes, 240=240... so our solution is correct.