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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
+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
+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
+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