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Tony's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tony $4.30 per pound, and type B coffee costs $5.70 per pound. This month, Tony made 177 pounds of the blend, for a total cost of $877.30. How many pounds of type A coffee did he use?

 Sep 23, 2020
 #1
avatar+28 
+1

Hi!
This problem uses a two equation system(I don't know the proper name).

 

First, we "turn words into math" as some people call it.
 

Let x = Type A Coffee
Let y = Type B Coffee

 

If he made 177 pounds, then the following must be true:

 

x + y = 177

 

Also, if Type A Coffee costs $4.30 a pound, and Type B Coffee costs $5.70 a pound, then the following also must be true:

 

4.30x + 5.70y = 877.30

 

Now, we make some like terms and combine the equations:

 

If we multiply the first equation by 4.3:

 

4.30x + 4.30y = 761.10

 

And now we subtract the second equation from the first:

 

4.30x + 4.30y = 761.10

4.30x + 5.70y = 877.30

 

-1.40y = -116.2

 

Divide by -1.40:

 

y = 83.

 

y equals the number of pounds of type b coffee, so we subtract 83 from 177.

 

I think you can do the rest yourself. :)

 

Hope this helps!

 Sep 23, 2020
 #2
avatar+986 
+1

-so:

 

877.30 = 4.30A + 5.70B.

 

A+B = 177.

 

 

Isolate A. 

 

A = (8773 - 57B)/43.

 

Substitute that ^^ into a:

 

(8773 -57B)/43 +B = 177.

 

8773-14B = 177

 

Isolate B:

 

B = 83

 

(8773 - 57*83)/43 = 94, 94 = A.

 Sep 23, 2020
edited by hugomimihu  Sep 23, 2020
 #3
avatar+27695 
+2

A = amount of type A                               cost = 4.3 A

B amount of type B =   177-A                  cost  = 5.7 (177-A)                 summed = 877.3

 

4.3A    +    5.7(177-A)        = 877.3      solve for A     then B = 177- A

 Sep 23, 2020

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