SOLUTION: coffee A, coffee B, and coffee C are combined to 52 lb batch of coffee. Twice as many pounds of coffee C are needed as coffee A. Coffee A is $15.99 per lb, coffee B is $12.45 per l

Question 927227: coffee A, coffee B, and coffee C are combined to 52 lb batch of coffee. Twice as many pounds of coffee C are needed as coffee A. Coffee A is $15.99 per lb, coffee B is $12.45 per lb and coffee C is $12.76 per lb. How many pounds of each coffee should be used to sell for $13.34 per lb?
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = lbs of A
y = lbs of B
z = lbs of C
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x + y + z = 52
z = 2x
15.99x + 12.45y + 12.76z = 13.34*52
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put the system of linear equations into standard form
---
x + y + z = 52
2x - z = 0
15.99x + 12.45y + 12.76z = 693.68
---
copy and paste the above standard form linear equations in to this solver:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
solution:
x = lbs of A = 11.125
y = lbs of B = 18.625
z = lbs of C = 22.25
---
now by substitution:
z = 2x
x + y + z = 52
15.99x + 12.45y + 12.76z = 13.34*52
---
x + y + 2x = 52
15.99x + 12.45y + 12.76*2x = 693.68
---
3x + y = 52
(15.99 + 12.76*2)x + 12.45y = 693.68
---
y = 52 - 3x
41.51x + 12.45y = 693.68
---
41.51x + 12.45(52 - 3x) = 693.68
41.51x + 12.45*52 - 12.45*3x = 693.68
(41.51 - 12.45*3)x = 693.68 - 12.45*52
x = (693.68 - 12.45*52)/(41.51 - 12.45*3)
x = 11.125
---
z = 2x
z = 2*11.125
z = 22.25
---
y = 52 - 3x
y = 52 - 3*11.125
y = 18.625
---
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solution by substitution:
x = lbs of A = 11.125
y = lbs of B = 18.625
z = lbs of C = 22.25
---
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