Question

Daniel buys 6 pounds of bird food and 12 pounds of cat food for $63. Katherine buys 14 pounds of bird food and 8 pounds of cat food for $72.

What is the cost of one pound of bird food?

Answer 1

The cost of one pound of bird food is $3.

Step-by-step explanation:

To find the cost per pound of bird food, we can set up a system of linear equations based on the information given. Let ( B ) represent the cost per pound of bird food and ( C ) represent the cost per pound of cat food.

For Daniel's purchase:

[ 6B + 12C = 63 ]

For Katherine's purchase:

[ 14B + 8C = 72 ]

Solving this system of equations, we find ( B = 3 ) and ( C = 3 ).

Therefore, the cost per pound of bird food (( B )) is $3.

In the first equation, we can express ( C ) in terms of ( B ):

[ 6B + 12(3) = 63 ]

[ 6B + 36 = 63]

[ 6B = 27 ]

[ B = 3 ]

So, the cost per pound of bird food is $3.

This result is consistent with the second equation:

[ 14(3) + 8(3) = 72 ]

[ 42 + 24 = 72 ]

Therefore, the solution ( B = 3 ) satisfies both equations, confirming that the cost of one pound of bird food is indeed $3.