Three varieties of coffee long dash— Coffee A, Coffee B, and Coffee C long dash— are combined and roasted, yielding a 51-lb
batch of coffee beans. Twice as many pounds of Coffee C, which retails for $9.95 per lb, are needed as Coffee A, which sells for $15.99 per lb. Coffee B retails for $13.21 per lb. How many pounds of each coffee should be used in a blend that sells for $12.82 per lb?
Let A, B and C be the number of pounds of each brand of coffee. A+B+C=51 (weight) which is 3A+B=51 because C=2A, B=51-3A 15.99A+13.21B+19.90A=51×12.82=653.82 (cost) I’ve used C=2A 35.89A+13.21B=653.82 Substitute for B: 35.89A+13.21(51-3A)=653.82 35.89A+673.71-39.63A=653.82 3.74A=19.89, A=117/22 pounds, B=771/22 pounds, C=117/11 pounds. Approximate weights are A: 5.32lb, B: 35.05lb, C: 10.64lb.
Answer: Use a compass to measure the length of AB. Draw an arc from point B (or point A) with that distance. Extend line AB through that arc and label the intersection as point C. AC is twice the length of AB.
