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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?

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cryssatemp

Answer: The price per pound of Brand Y dog food is [tex]\$1.2[/tex]

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 [tex]\$ 8.40[/tex]:

[tex]8X+1Y=\$8.40[/tex] (1)

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

[tex]16X+8Y=\$24.40[/tex] (2)

Now we have two equations with two unknowns and we need to find [tex]Y[/tex].

Multiplying eqquation (1) by [tex]-2[/tex]:

[tex]-16X-2Y=-\$16.8[/tex] (3)

Adding (2) and (3):

[tex]6Y=\$7.2[/tex] (4)

Isolating [tex]Y[/tex]:

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

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