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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?


Write an equation. Let x represent the cost of one of Tanya's items. Solve the equation. Show your work. Check your solution. Show your work. State the solution in complete sentences.

Respuesta :

x=cost of one of Tanya´s items.
Tanya spent: 3x
Tony spent:4(x-2.25)

We can suggest this equation:
3x=4(x-2.25)

We solve this equation:
3x=4(x-2.25)
3x=4x-9
3x-4x=-9
-x=-9
x=9

The individual cost of each person´s item would be:
cost of one of Tanya´s items=x=9
Cost of one of Tony´s items=(x-2.25)=6.75

Answer: the cost of one of Tanya´s items was $9, and the cost of one of Tony´s items was $6.75, the equation used was [  3x=4(x-2.25)  ] .

We check it out our answer: 

Tanya spent: 3x=3(9)=27
Tony spent:4(x-2.25)=4(9-2.25)=4(6.75)=27

Because Tanya spent the same amount of money than Tony, and Tanya bought 3 items and Tony bought 4 items, this solution is right. 


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