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?

Question

Dante Velez

Mathematics

23 April, 18:16

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?

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Porter Howell · Answer 1

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.