Question

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 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 individual cost of Tanya's items is $9

the individual cost of Tony's items is $6.75

Step-by-step explanation:

Let x represent the individual cost of Tanya's items.

Let y represent the individual cost of Tony's items.

Each of the items that Tony bought was $2.25 less than the items Tanya bought. It means that

x = y + 2.25

Tanya bought 3 items that each cost the same amount. Tony bought 4 items that each cost the same amount. Both Tanya and Tony paid the same amount of money. It means that

3x = 4y- - - - - - - - - -1

Substituting x = y + 2.25 into equation 1, it becomes

3(y + 2.25) = 4y

3y + 6.75 = 4y

4y - 3y = 6.75

y = 6.75

x = y + 2.25 = 6.75 + 2.25

x = 9

Answer 2

Answer:

The individual cost of each person’s items was $ 9 for Tanya and $6.75 for Tony

Step-by-step explanation:

First we have to find 2 equations to express the problem

x = value of each item

y = total amount of money

3x = y

4 ( x - 2.25 ) = y

we replace the y by (3x) in the second equation and obtain the value of x

4 ( x - 2.25 ) = y

4 ( x - 2.25 ) = 3x

4x - 9 = 3x

4x - 3x = 9

x = 9

9 - 2.25 = 6.75

this means that the individual cost of each person’s items was $ 9 for Tanya and $6.75 for Tony