The Coffee Counter charges $9.00 per pound for Kenyan French Roast coffee and $8.00 per pound for Sumatran coffee. How much of each type should be used to make a 20-lb blend that sells for $8.40 per pound?
Here are the 2 equations (or system of equations) I created:
K = lbs of Kenyan French Roast coffee
S = lbs of Sumatran coffee
k + s = 20
9k + 8s = 8.40
I then multiplied the top equation by -8 so I could do the elimination method to solve.
That got made k+s=20 into -8k + -8s = -160.
Of course, when I added those two equations together, I got k = -151.6, which couldn't possibly be right.
Are my two equations right, and can you see where I went wrong?
Thanks,
¢¾ Valeria ¢¾
your final cost for the 20 lb blend will be $168. K=$9 and S=$8. you have to find out how many pound of k plus how many pounds of s will equal 20 pounds and $168
You are making the same error as you did in your post at 5:26 pm
make your last equation 9k + 8s = 8.40(20)
(I got k=8, s = 12)
Your equations are correct, but there was a mistake in your calculation when you multiplied the first equation by -8.
The correct multiplication should be:
-8(k + s) = -8(20)
-8k - 8s = -160
So, your system of equations should be:
-8k - 8s = -160
9k + 8s = 8.40
Now, you can use the elimination method by adding the two equations together:
(-8k - 8s) + (9k + 8s) = -160 + 8.40
This simplifies to:
k = -151.6 + 8.40
k = -143.2
It seems there was an error when adding the equations together. Please double-check your calculations and try again.
Hi Valeria! It looks like your equations are correct, but you made a small error when multiplying the top equation by -8. Let me show you the correct steps to solve the problem using the elimination method.
Here are your equations:
1) K + S = 20
2) 9K + 8S = 8.40
To eliminate one variable, we'll multiply the top equation (equation 1) by 8 and the bottom equation (equation 2) by -1:
3) 8K + 8S = 160 (equation 1 multiplied by 8)
4) -9K - 8S = -8.40 (equation 2 multiplied by -1)
Now, let's add equation 3 and equation 4 together:
5) -K = 151.6
At this point, the signs of your equation have reversed because of the multiplication. Now, we can solve for K by multiplying both sides by -1:
6) K = -151.6
However, it seems that there might be a mistake earlier in the calculations. Can you please recheck your previous steps to identify where the error occurred? Remember to correctly distribute the negative sign when multiplying equations.
Once you find and correct the error in your calculations, you should get a positive value for K and S that makes sense in the context of the problem. Let me know if you have any further questions or if there's anything else I can help you with!