Question

3 pounds of coffee and 8 pounds of tea cost 1080 rs and 5 pounds of coffee and 6 pounds of tea cost 1140 rs find the cost of coffee and tea per pound

Answer 1

Answer:

Cost of coffee per pound = 120 Rs

Cost of tea per pound = 90 Rs

Step-by-step explanation:

Let x be the price of coffee per pound. Let y be the price of tea per pound.

It is given that 3 pounds of coffee +  8 pounds of tea = 1080 Rs. Therefore:

3x + 8y = 1080    (1)

It is also given that 5 pounds of coffee + 6 pounds of tea = 1140. Therefore:

5x + 6y = 1140    (2)

Now solve equations (1) and (2) simultaneously:

$3x + 8y=1080\\5x+6y=1140\:\:(*\frac{-3}{5} )\\ \\\\3x+8y=1080\\-3x-\frac{18}{5}y=-684$

Add the two equations:

$4.4y=396\\y=90$

Substitute by y=90 in equation (1):

$3x + 8(90) = 1080\\3x=360\\x=120$

Answer 2

Answer:

Coffee = Rs 120 per pound

Tea = Rs 90 per pound

Step-by-step explanation:

Define x and y:

Let the cost of coffee be Rs x per pound

Let the cost of tea be Rs y per pound

Form the equations:

3x + 8y = Rs 1080 ------------  [ 1 ]

5x + 6y = Rs 1140  ------------  [ 2 ]

[ 1 ] x 5 : 15x + 40y = 5400 ------------  [ 3 ]

[ 2] x 3 : 15x + 18y = 3420  ------------  [ 4 ]

[3] - [4]:

22y = 1980

y = 90  ------------   sub into [ 1 ]

3x + 8(90) = 1080

3x + 720 = 1080

3x = 360

x = 120

Find the cost:

1 pound of coffee = x = Rs 120

1 pound of tea = y = Rs 90

Answer: Coffee is at Rs 120 per pound and Tea Rs 90 per pound