Coffee Types Explained
Two math problems (find variables, set up the two equations, solve)?
I have two equations, and I find myself at a loss to setting them up. please not only ANSWER but explain how you got your answer. actually, i’d rather have help being told how to set them up, then having the answer.
problem 1.
On a canoe trip down the Spoon River, Jim is able to travel 10 miles downstream with a current in 2.5 hours. On a return trip upstream back to where his truck is parked, it takes Jim 3.5 hours. How fast is Jim’s canoe traveling, and how fast is the current on the river that day (explain what the variables you use represent).
Problem 2.
The owner of jumping lava bean is making a blend of two types of coffees to sell in his coffee shop. she wants to have 60 pounds of the blend and sell it for %7.25 per pound . She will be mixing a columbian coffee that sells for $6.90 per pound with an Ethiopian coffee that sells for $7.50 per pound. How many pounds of each type of coffee wil she need?
that’s supposed to be a dollar sign, not a percent.
1) Let V = Jim’s speed in still water.
Let C = Speed of the current
His speed downstream = V + C
His speed upstream = V – C
Downstream:
(1) D = rt = (V + C)(2.5) = 10
(2) D = rt = (V – C)(3.5) = 10
(1) 2.5V + 2.5C = 10
(2) 3.5V – 3.5C = 10
(1) times 2 : 5V + 5C = 20
(1) divided by 5: V + C = 4
(2) times 2: 7V – 7C = 20
(2) divided by 7: V – C = 20/7
(1) ……………….V + C = 4
Add:…………….2V = 48/7
V = 24/7
(1) V + C = 4
24/7 + C = 4
C = 4 – 24/7
C = 4/7
2)Let C = the number of pounds of Columbian coffee required.
Then the number of pounds of Ethiopian coffee required is 60 – C.
The cost of the Columbian coffee is $6.90C
The cost of the Ethiopian coffee is $7.50(60 – C)
Together the cost will add up to: $7.25(60).
The equation is:
6.90C + 7.50(60 – C) = 7.25(60)
6.90C + 450 – 7.50C = 435
-0.6C = – 15
C = 25 pounds
E = 60 – 25 = 35 pounds
Kona Coffee Explained
