Math question…help please?
A coffee manufacturer uses Colombian and Brazilian coffee beans, to produce two blends, robust and mild.A pound of the robust blend requires 12 oz of Colombian beans and 4 oz of Brazilian beans. A pound of the mild blend requires 6 oz of the Colombian beans and 10 oz of the Brazilian beans. Coffee is shipped in 99-pound burlap bags. The company has 47 bags of Colombian beans and 25 bags of Brazilian beans on hand. How many pounds of each blend should they produce in order to use all the available beans?
Using:
1 robust = (3/4) columbian + (1/4) brazian
1 mild = (3/8) columbian + (5/8) brazilian
Given:
47 * 99lbs of columbian = 4653 columbian
25 * 99lbs of brazilian = 2475 brazilian
Thus:
Total coffee = (47+25)*99 = 7128
Let X = pounds of robust to make.
Let (7128-X) = pounds of mild to make.
X * (robust) + (7128-X) * (mild) = 4653 columbian + 2475 brazilian
Let C = pounds of columbian
Let B = pounds of brazilian
Rewriting using C and B (for simplicity):
X * ((3/4)C + (1/4)B) + ((7128-X) * ((3/8)C + (5/8)B)) = 4653C + 2475B
Solve for X:
(3/4)CX + (1/4)BX + 2673C -(3/8)CX + 4455B – (5/8)BX = 4653C + 2475B
(3/4)CX + (1/4)BX -(3/8)CX -(5/8)BX + 2673C + 4455B = 4653C + 2475B
x[(3/4)C + (1/4)B -(3/8)C -(5/8)B] + 2673C + 4455B = 4653C + 2475B
x[(3/4)C + (1/4)B -(3/8)C -(5/8)B] + 2673C + 4455B = (4653-2673)C + (2475-4455)B
x[(3/8)C - (3/8)B] = (4653-2673)C + (2475-4455)B
x[(3/8)C - (3/8)B] = 1980C -1980B
x = (1980C -1980B)/((3/8)C – (3/8)B)
x = 8(1980C -1980B)/(3C – 3B)
x = 8(660C -660B)/(C – B)
x = 5280(C -B)/(C – B)
x = 5280
Solve for mild:
mild = 7128-5280 = 1848
To verify, check the use of columbian coffee:
5280*(3/4) + 1848*(3/8) = 47*99
3960 + 693 = 4653
4653 = 4653
check.
Now check the use of brazilian coffee:
5280 * (1/4) + 1848*(5/8) = 25*99
2475 = 2475
check.
Answer:
Produce 5280 pounds of robust coffee and 1848 pounds of mild
.
|
|
Authentic (Burlap or Burlap Similar) Coffee Bag $3.85 These coffee bags hold between 100-155 lbs. of green coffee. You can use them for gardening, for decoration, as a laundry bag — you name it. They are super cool, and each bag has the markings of the country of import. We buy coffee from all over the world, so your bag may be from anywhere! Due to heavy volume for this item we can not guarantee specific country of origins for you…. |
|
|
Jamaica Blue Mountain Coffee 2oz Burlap Bag ground $24.16 Jamaica Blue Mountain Coffee 2oz Burlap Bag ground – Jamaica Blue Mountain coffee is one of the most sought after coffees in the world. This “Java of Kings” has been satisfying coffee connoisseurs around the globe for more than two centuries and is famous for its exquisite flavor, good acidity, a clean refined taste,unusual sweetness, excellent body and intense bold aroma. This extraordinary cof… |
|
|
High Quality Jute Drawstring Bag Eco Friendly Natural 10×14- Set of 6 $9.99 Perfect packaging alternative for items that requires a more natural look. It has drawstring closure at the top of the bag. 100% Jute fabric bag with jute rope can be used packing, gift bag and is reusable. The bag have competitive price with high quality…. |
|
|
Wallmonkeys Peel and Stick Wall Decals – Burlap Sack of Coffee Beans against Dark Wood – Removable Graphic WallMonkeys wall graphics are printed on the highest quality re-positionable, self-adhesive fabric paper. Each order is printed in-house and on-demand. WallMonkeys uses premium materials & state-of-the-art production technologies. Our white fabric material is superior to vinyl decals. You can literally see and feel the difference. Our wall graphics apply in minutes and won’t damage your paint or l… |
|
|
Wallmonkeys Peel and Stick Wall Decals – Coffee Beans Close-up – Removable Graphic WallMonkeys wall graphics are printed on the highest quality re-positionable, self-adhesive fabric paper. Each order is printed in-house and on-demand. WallMonkeys uses premium materials & state-of-the-art production technologies. Our white fabric material is superior to vinyl decals. You can literally see and feel the difference. Our wall graphics apply in minutes and won’t damage your paint or l… |
|
|
Wallmonkeys Peel and Stick Wall Decals – Sheet of Old Paper with Spilled Coffee Motif – Removable Graphic WallMonkeys wall graphics are printed on the highest quality re-positionable, self-adhesive fabric paper. Each order is printed in-house and on-demand. WallMonkeys uses premium materials & state-of-the-art production technologies. Our white fabric material is superior to vinyl decals. You can literally see and feel the difference. Our wall graphics apply in minutes and won’t damage your paint or l… |
|
|
ColcaSac Juan Valdez iPad Sleeve $60.00 … |
|
|
ColcaSac Juan Valdez iPhone Sleeve $20.00 … |
|
|
Jamaica Blue Mountain Coffee Jamaica Blue Mountain “Wallenford Estate” has been satisfying coffee connoisseurs around the globe for more than two centuries and is famous for its exquisite flavor, balanced acidity, a clean refined taste, unusual sweetness, excellent body and intense bold aroma. Simply Amazing!… |
|
|
High Quality Cotton Muslin Bags Wedding Gift Bags 8×12 inch ($1.75 each) Pack of 10 $17.52 Simple and unbleached 100% cotton muslin bags with a drawstring. Very useful for brewing large pots of tea, infusing bath herbs, for poultices, food preparation, and a variety of other uses.Makes a great gift or favor bag to bring out the natural earthly feeling. Small Dimensions- 3″ x 4″… |
