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Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television. Each Model P television sold for $p and each Model Q television sold for $q. The average (arithmetic mean) selling price of the 40 televisions was $141. How many of the 40 televisions were Model P televisions?

Respuesta :

Answer:

[tex]\frac{5640-40p}{p-q}[/tex]

Step-by-step explanation:

Here, the total number of television = 40,

Let x be the number of P television,

So, the number of Q television = (40 - x)

Now, the price of each P television is $ p,

∴ The total price of P televisions = xp dollars,

Also, the price of each Q television is $ q,

∴ The total price of Q televisions = (40-x)q dollars,

Thus, the total price of 40 television = xp + (40-x)q = x(p-q) + 40q,

Hence, the average price = [tex]\frac{\text{Total price}}{\text{Number of television}}[/tex]

[tex]=\frac{x(p-q)+40q}{40}[/tex]

According to the question,

[tex]\frac{x(p-q)+40q}{40}=141[/tex]

[tex]x(p-q)+40q=141\times 40[/tex]

[tex]x(p-q) = 5640 - 40q[/tex]

[tex]\implies x=\frac{5640-40p}{p-q}[/tex]

Therefore, there were [tex]\frac{5640-40p}{p-q}[/tex] P model televisions.

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