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PLEASE PLEASE PLEASE I NEED HELP ASAP THIS IS DUE TOMORROW AHHH 27 POINTS AND BRAINLIEST!!!

At a bargain store, Tanya bought 5 items that each cost the same amount. Tony bought 6 items that each cost the same amount, but each was $1.75 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?
(a) Write an equation. Let x represent the cost of one of Tanya's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.

PLEASEEEEEE HELPPP D=

Respuesta :

Let x be the price of Tanya's item. Tanya spent 5x, because she bought 5 of them.

The cost of Tony's item is x-1.75, because the price is 1.75 less than Tanya's. He spent 6(x-1.75), because he bought 6 of them.

They spent the same amount of money, so we have

[tex]5x=6(x-1.75) \iff 5x=6x-10.5 \iff -x=-10.5\iff x=10.5[/tex]

So, Tanya's item costs 10.5, and Tony's item costs 8.75.

In fact, we have

[tex]10.5\cdot 5 = 52.5 = 8.75\cdot 6[/tex]

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