Model P televisions made up 12 of the 40 televisions when Quick Sell outlet sold a total of 40 television, each of which was either a model P television or a model Q television.
Price plus quantity equals revenue.
Let x be the quantity of sold TVs of model p.
40 - x units of the model q TV would have been sold.
Profits from model p TV sales are
px
Sales of the type q TV bring in money.
(40 - x)q
Total income equals px plus (40 - x)q
The average price calculation formula is written as
Total revenue / total number of TVs sold equals average price.
The 40 televisions sold for an average (arithmetic mean) price of $141. It follows that
141 = (px + (40 - x)q)/40
141 × 40 = px + (40 - x)q
5640 = px + (40 - x)q
p = q - 30
5640 = x(q - 30) + (40 - x) (40 - x)
q
30x + 40q - xq = 5640
5640 = - 30x + 40q
Since q = 120,
5640 = - 30x + 40 × 120
5640 = - 30x + 4800
5640 - 4800 = - 30x
840 = - 30x
x = 840/- 30 = - 28
Q cannot equal 120 since x cannot be negative.
Again,
5640 = px + (40 - x)q
If q = 30 + p, then
5640 = px + (40 - x)(30 + p)
5640 = px + 1200 + 40p - 30x - px
5640 = 1200 + 40p - 30x
Therefore,
If p = 120, then
5640 = 1200 + 40 × 120 - 30x
5640 = 6000 - 30x
30x = 6000 - 5640
30x = 360
x = 360/30
x = 12
Therefore, out of 40 televisions 12 tv are of model p
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