3. At a bargain store, Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. Both Tanya and Tony paid the same amount of money. What was the individual cost of each person's items?

Tayna bought 3 items that all share the same price.

So, we will call this 3x. Where x = a price.

Then Tony bought 4 items that each cost the same amount, but each was $2.25 less than the items that Tanya bought. So, we will call this 4 (x - 2.55).

We put parentheses around the x and 2.55 because x = the price and Tony's items all are $2.55 less than Tanya's.

Now lets put the equation together and solve this.

3x = 4 (x - 2.55)

It has an equal sign because both paid the same amount of money.

Let's do the distributive law of property with the 4.

3x = 4x - 10.2

-x = - 10.2

Transpose the 4x.

Because both are negative, it's actually positive.

x = 10.2

Now let's substitute the x in the equation to see if it fits!

3 (10.2) = 4 (10.2 - 2.55)

After doing the work it comes out as 36=36.

But now back to the original question. What is the individual price for each person?

We know that Tayna's price for each item is $10.2. But what about Tony's?

Well in the question it said it's $2.55 less than Tayna's items.

$10.2 - $2.55 = $7.65

So, each of Tony's items is $7.65.