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An antique store increases all of its prices by $40\%$, and then announces a $25\%$-off-everything sale. What percent of the original prices (before the increase) are the new prices? show work plz! It's not 5% by the way

Respuesta :

MrRoyal

Answer:

105%

Step-by-step explanation:

We'll analyse the question one step at a time

Let the original price be x.

Let y be the 40% increase

[tex]y =x + 40\% *x[/tex]

Express as decimal

[tex]y =x + 0.40 x[/tex]

[tex]y =1.40x[/tex]

Let z be the 25% off sale

[tex]z = (1 - 25\%) * y[/tex]

Express as decimal

[tex]z = (1 - 0.25) * y[/tex]

[tex]z = (0.75) * y[/tex]

[tex]z = 0.75y[/tex]

Substitute 1.40s for y

[tex]z = 0.75*1.40x[/tex]

[tex]z = 1.05x[/tex]

Express 1.05 as a fraction

[tex]z = 105\% * x[/tex]

The percentage is 105%

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