Pre-Calc equation (Systems of Linear Equations)

Question

Three varieties of coffee— Coffee A, Coffee B, Coffee C— are combined and roasted, yielding a 54-lb batch of coffee beans. Twice as many pounds of Coffee C, which retails for $12.76 per lb, are needed as Coffee A, which sells for $14.99 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 $13.34 per lb?

Answer 1

We have lbs of coffee A, B, and C, so that

A+B+C=54

And we also know that there is twice as much C as A or

C=2A

Multiplying price rate with weight give total price for each quantity

total price=14.99A+13.21B+12.76C=13.34

we can make the substitution

14.99A+13.21B+12.76(2A)=13.21B+14.99A+25.52A=13.21B+40.51A=13.34 (i)

but we can also do this for the first equation

A+B+(2A)=B+3A=54 (ii)

We have an ideal situation with 2 variables and 2 equations. Simply substituting one variable gives

the solution.