Question

Bill has $30 to spend on pet supplies. Dog food costs $3 and dog treats cost $2. Write a 2-variable inequality that represents this situation. Determine at least 1 ordered pair that satisfies this scenario.

Answer 1

We know that each dog food unit costs $3, and each dog treat costs $2.

Let's define the variables:

x = units of dog food that Bill buys

y = units of dog treat that Bill buys.

The total cost of the purchase will be:

cost = x*$3 + y*$2

And we know that Bill wants to spend $30, then the equation is:

$30 = x*$3 + y*$2

Now we could isolate one of the variables in one side of the equation, for example, let's isolate the "y".

$30 - x*$3 = y*$2

$30/$2 - x*($3/$2) = y

15 - (3/2)*x = y

Now we have the linear equation:

y = -(3/2)*x + 15

To determine an ordered pair, we just can replace the x by a number, like x = 2, that would mean that Bill bought 2 units of dog food.

in this case:

y = -(3/2)*2 + 15 = -3 + 15 = 12

y = 12

This ordered pair is (2, 12)