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Faye and Rudy decided they wanted to save up money to buy a new TV. To do so, they began to stop eating out and only eat at home for four weeks. Faye managed to save two times three more dollars than Rudy, but then spent 1⁄3 of what Rudy saved on a birthday dinner. She ended up saving $278. How much money did Rudy save? If they spent all their money on the TV, how much did it cost?

Respuesta :

Answer:

The amount saved by Rudy was, $181.33.

The cost of TV was $459.33.

Step-by-step explanation:

Let the amount saved by Rudy be, x.

Then the amount saved by Faye was, [tex]2(x+3)[/tex].

It is provided that Faye spent 1⁄3 of what Rudy saved on a birthday dinner.

Compute the remaining amount that Fave has now as follows:

Remaining Amount = 2 (x + 3) - x/2

                                [tex]=2x+6-\frac{x}{2}\\[/tex]

                                [tex]=\frac{4x+12-x}{2}\\[/tex]

                                [tex]=\frac{3x+12}{2}[/tex]

It is provided that the total money saved by Faye was $278.

Compute the value of x as follows:

[tex]\frac{3x+12}{2}=278\\3x+12=556\\3x=544\\x=181.33[/tex]

Thus, the amount saved by Rudy was, $181.33.

Compute the cost of TV as follows:

Cost of TV = Savings of Rudy + Savings of Faye

                  = $181.33 + $278

                  = $459.33

Thus, the cost of TV was $459.33.

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