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?
+28 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!
+1008 -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.
+37159 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
