Linear Equation problems

Question

Homer and Marge run out of coffee, Homer likes the Dark roast which cost 8.50 dollars per kg and Marge likes the light roast that is 9.20 dollars per kg. They buy a bag the that is a mix, 5.5 kg which costs 48.50 dollars. How many kg of each type went into the mix?

Answer 1

We are trying to solve for 2 variables here:

1. The number of kg of Dark roast

2. The number of kg of Light roast

 

So let's assume:

 

D = number of kg of Dark roast

L = number of kg of Light roast

 

We know the total of weigh of the mix is 5.5 kg so:

D + L = 5.5 (Equation 1)

 

And we know that the total cost of mix is 48.5 dollars, so:

8.5 * D + 9.2 * L = 48.50 (Equation 2)

 

Now solve for the system of equations

 

We get the following from solving for D in Equation 1

D = 5.5 - L (Equation 3)

 

Substitute D in the second equation with the above value and we get:   

 

8.5 * (5.5 - L) + (9.2 * L) = 48.50

 

Now solve for L:

46.75 - 8.5L + 9.2L = 48.50

9.2L - 8.5L = 48.50 - 46.75

0.7L = 1.75

L = 1.75/0.7

L = 2.5

 

Now substitute L back in Equation 3 and get: 

D = 5.5 - 2.5

D = 3

 

3 kg of Dark roast

2.5 kg of Light roast