Question

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?

Answer 1

Answer: The answer above is actually incorrect, the answer is that each item was of Tanya's was $9, and each item of Tony's was $6.75.

Explanation:

So, the answer above says that it was $7.65 per item, but if we run that number through the equation, it proves false:

(Using x as the cost of one of Tanya's items)

3x = 4(x-2.25)

3*7.65 = 4(7.65 - 2.25)

22.95 = 4 * 5.4

22.95 does not equal 21.6, so this is false.

All of the steps they took were correct, but at one point, they accidentally put 2.55 instead of 2.25, so let's now test $9.

3x = 4(x-2.25)

3*9 = 4(9-2.25)

27 = 4 * 6.75

27 = 27

So, the cost of each of Tanya's items were $9 each, so let's find Tony's per item cost:

We know from the equation that x - 2.25 = T (T representing per item cost for Tony)

9 - 2.25 = 6.75

Let's run through this one more time:

3*9 = 4 * 6.75

27=27

Answer 2

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.