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Mr. Thomas spent $1,600 of his savings on a television set and 2/5 of the remainder on a refrigerator. He had 1/3 of his original amount of savings left. What was the cos of the refrigerator?

Respuesta :

Answer:

The amount spent on the refrigerator is $ 800 .

Step-by-step explanation:

Given as :

The amount spent on television = $ 1600

Le The total amount in the account = $ A

so, The amount left in account after spent on television = $ A - $ 1600

The amount spent on refrigerator = [tex]\frac{2}{5}[/tex] × ( A - 1600 )

The amount left in his saving account = [tex]\frac{1}{3}[/tex] × A

Now, According to question

A - ( 1600 +  [tex]\frac{2}{5}[/tex] × ( A - 1600 ) ) =  [tex]\frac{1}{3}[/tex] × A

Or, A -  [tex]\frac{1}{3}[/tex] × A = 1600 +   [tex]\frac{2}{5}[/tex] × ( A - 1600 )

Or, [tex]\frac{2}{3}[/tex] × A = 1600 + [tex]\frac{2}{5}[/tex] × A - [tex]\frac{2}{5}[/tex] × 1600

or,  [tex]\frac{2}{3}[/tex] × A -  [tex]\frac{2}{5}[/tex] × A = 1600 - 640

Or,  [tex]\frac{10 - 6 }{15}[/tex] × A = 960

or,  [tex]\frac{4}{15}[/tex] × A = 960

∴ A = [tex]\frac{960\times 15}{4}[/tex]

I.e A = 3600

So, The amount in the saving account  is $3600

∵ , The amount spent on refrigerator = [tex]\frac{2}{5}[/tex] × ( 3600 - 1600 )

Or,  The amount spent on refrigerator = [tex]\frac{2}{5}[/tex] × 2000

I.e  The amount spent on refrigerator = $ 800

Hence The amount spent on the refrigerator is $ 800 . Answer

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