Blending spice:
Spice of life sells ground sumac for $1.35per ounce and ground thyme for $1.85 per ounce. Aman wants to make a 20 oz Zahtar seasoning blend using the two spices that sells for $1.65 per ounce. How much of each spice should Aman use?
I know that there are 28 grams in a pound i am lost when it comes to this problem
Please help!
1.35 s + 1.85 t = 1.65 * 20
s + t = 20 so s = (20-t)
===========================
1.35 (20-t) + 1.85 t = 33
solve for t, go back and get s
Sumac: 21.9 oz
Thyme: 1.9 oz
To solve this problem, we can set up a system of equations. Let's say Aman uses x ounces of sumac and y ounces of thyme in the blend.
1. The cost equation:
The total cost of the blend can be expressed as the sum of the individual spice costs. Since the cost of the blend is $1.65 per ounce, we can write the equation:
1.35x + 1.85y = 1.65 * 20
2. The quantity equation:
The total quantity of the blend is 20 ounces, so we have the equation:
x + y = 20
Now, we have a system of two equations:
1.35x + 1.85y = 33
x + y = 20
We can solve this system using various methods, such as substitution or elimination. Here, we will use the substitution method.
1. Solve the second equation for x:
x = 20 - y
2. Substitute x in the first equation:
1.35(20 - y) + 1.85y = 33
27 - 1.35y + 1.85y = 33
0.50y = 6
y = 12
3. Substitute y back into the second equation to find x:
x + 12 = 20
x = 8
Therefore, Aman should use 8 ounces of ground sumac and 12 ounces of ground thyme in the Zahtar seasoning blend.