Bully's dog treats

Question

Bully buys 3 raw hide treats and 2 beer-flavored bones and pays $1.78.  Changing his mind, he exchanges a beef-flavored bone for another raw hide treat and has to pay an additional 16 cents.  What is the price of a single raw hide treat?

Answer 1

We know that 3 raw hide and 2 beef (I'm assuming beef, not beer) costs $1.78

 

If we say r = cost of raw hide and b = cost of beef then:

 

3r + 2b = $1.78

 

Now we change our mind and swap out a beef for another raw hide and it costs $.16 more.  So now we can say:

 

4r + b = $1.78 + $.16

4r + b = $1.94

 

Now we can find the value of b in terms of r

 

b = $1.94 - 4r

 

We can use that value in our first equation and substitute it:

 

3r + 2b = $1.78

3r + 2(1.94-4r) = 1.78

 

Now you can solve for r

Answer 2

Let's express this as formulas, using variable 't' for treats, and 'b' for bones.

 

First transaction:

3t + 2b = 1.78

Changed his mind:

4t + 1b = 1.94

1b = 1.94 - 4t

 

Now we know that one bone is equal to the expression '1.94 - 4t', and can substitute this in the original formula.

3t + 2b = 1.78

3t + 2(1.94 - 4t) = 1.78

3t + 3.88 - 8t = 1.78

-5t = -2.10

t = 0.42

 

One treat is equal to $0.42.  If needed, take one step further to find the price of one bone.

3t + 2b = 1.78

3(0.42) + 2b = 1.78

1.26 + 2b = 1.78

2b = 0.52

b = 0.26

 

This helps proof the $0.16 price differential between items (treats are $0.42, less bones at $0.26).