Question

At a pet store the total cost of 8 pounds of Brand X dog food and 1 pound of Brand Y dog food is $8.40, including tax. The total cost of 16 pounds of Brand X dog food and 8 pounds of Brand Y dog food is $24.00, including tax. What is the price per pound of Brand Y dog food?

Answer 1

Answer: The price per pound of Brand Y dog food is $\ 1.2$

Step-by-step explanation:

We have to brands of dog food (Brand X and Brand Y).

So, firstly we are told the total cost of 8 pounds of Brand X and 1 pound of Brand Y $\ 8.40$:

$8X+1Y=\ 8.40$ (1)

Then, we are told the total cost of 16 pounds of Brand X and 8 pounds of Brand Y $is 24.00$:

$16X+8Y=\ 24.40$ (2)

Now we have two equations with two unknowns and we need to find $Y$.

Multiplying eqquation (1) by $-2$:

$-16X-2Y=-\ 16.8$ (3)

Adding (2) and (3):

$6Y=\ 7.2$ (4)

Isolating $Y$:

$Y=\ 1.2$ (5) This is the price per pound of Brand Y dog food