SOLUTION: Tom's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tom $5.10 per pound, and type B coffee costs $4.05 per pound. This month, Tom made 135
Question 767179: Tom's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tom $5.10 per pound, and type B coffee costs $4.05 per pound. This month, Tom made 135 pounds of the blend, for a total cost of $624.45 . How many pounds of type B coffee did he use? Found 2 solutions by ramkikk66, mananth:Answer by ramkikk66(644) (Show Source):
Tom's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Tom $5.10 per pound, and type B coffee costs $4.05 per pound. This month, Tom made 135 pounds of the blend, for a total cost of $624.45 . How many pounds of type B coffee did he use?
Ans:
Let Tom use x pounds of B coffee. That means he used (135 - x) pounds of A coffee.
Cost of B coffee = x*4.05
Cost of A coffee = (135 - x)*5.1 = 688.5 - 5.1*x
Total cost = 4.05*x + 688.5 - 5.1*x = 624.45
Simplifying
688.5 - 1.05*x = 624.45
1.05*x = 64.05
x = 61
135 - x = 74
So he used 61 pounds of type B and 74 pounds of type A coffee in the blend.
:)
1.00 x + 1.00 y = 135.00 .............1
Total value
5.10 x + 4.05 y = 624.45 .............2
Eliminate y
multiply (1)by -4.05
Multiply (2) by 1.00
-4.05 x -4.05 y = -546.75
5.10 x + 4.05 y = 624.45
Add the two equations
1.05 x = 77.70
/ 1.05
x = 74.00
plug value of x in (1)
1.00 x + 1.00 y = 135.00
74.00 + y = 135.00
y = 135.00-74.00
y = 61.00
y = 61.00
x= 74.00 pounds type A
y= 61.00 pounds Type B
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