Algebra word problem help

Question

David's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs David $5.75per pound, and type B coffee costs $4.45per pound. This month, David made 176 pounds of the blend, for a total cost of  $891.10

. How many pounds of type A coffee did he use?

Answer 1

This is a system of equations problem with two unknowns being the number of pounds of each type of coffee being Type A and Type B

 

Let A = the number of pounds of Type A coffee

Let B = the number of pounds of Type B coffee

 

Write the system of equation in which are:

 

A + B = 176

 

5.75A + 4.45B = 891.10

 

Since the question is how many pounds of Type A coffee was used, I would solve the system of equations by eliminating the the variable B. There are two ways you could do this: one by substitution, or by elimination of variables. I choose elimination of variables because it is less cumbersome. 

 

The first step is to multiply the first equation by 4.45, and put it under the second equation en which is:

 

5.75A + 4.45B = 891.10

4.45A + 4.45B = 176*4.45 = 783.20

 

Subtract the two equations in which gives:

 

1.3A = 107.9 Divide both sides of the equation by 1.3 to solve for A.

 

There were ____ pounds of Type A coffee he used.