24 lbs of coffee P and 25 lbs of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X?
A. 10
B. 20
C. 30
D. 40
D. 45
Make Coffee X and Coffee Y
P:V in coffee X is 4:1
P:V in coffee Y is 1:5
X + Y = 49
System of Equations
P1 + V1 = X (eq.1)
P2 + V2 = Y (eq.2)
P1 + P2 = 24 (eq.3)
V1 + V2 = 25 (eq.4)
P1 = (4/5)x
P2 = (1/6)y
V1 = (1/5)x
V2 = (5/6)y
---
(4/5)x + (1/6)y = 24
(1/6)y = 24 - (4/5)x
y = 144 - (24/5)x
(1/5)x + (5/6)y = 25
---
(1/5)x + (5/6)(144 - (24/5)x) = 25
(19/5)x = 95
x = 25
---
Y = 49 - x
Y = 24
---
P1 = (4/5)(25) = 20
P2 = (1/6)(24) = 4
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