Question

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 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?

1) the model p televisions sold for $30 less than the model q televisions
2) either p=120 or q=120

Answer 1

Answer: 12 of the 40 televisions were model p televisions

Explanation:

Revenue = price × quantity

Let x represent the number of the model p TV sold

The number of model q TV sold would be 40 - x

Revenue from model p TV sold is

px

Revenue from model q TV sold is

(40 - x)q

Total revenue = px + (40 - x)q

The formula for determining average price is expressed as

Average price = total revenue/total number of TV sold.

The average (arithmetic mean) selling price of the 40 televisions was $141. This means 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)q

5640 = xq - 30x + 40q - xq

5640 = - 30x + 40q

If q = 120, then

5640 = - 30x + 40 × 120

5640 = - 30x + 4800

5640 - 4800 = - 30x

840 = - 30x

x = 840/- 30 = - 28

since x cannot be negative, then q is not equal to 120

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

Answer 2

The number of the television sets that is model p is 12

Explanation:

Here we have total number of television sold = 40

The model p televisions sold for $30 less than the model q televisions

That is $P = $q - $30

Therefore

Let the quantity of the model p sold be X

Let the quantity of the model q sold be X

Therefore

x + y = 40

Total cost of the television = 40 * 141 = $5640

Therefore, 120*x + 90*y = 5640

Plugging in x = 40 - y in the above equation we get

4800 - 30y = 5640 or

y = -28 and

x = 68

If we put y = 40 - x we get

30x + 3600 = 5640

If we put

120*x + 150*y = 5640.........(3)

we get

x = 12 and y = 28

Therefore, since the model p sold for $30 less than the model q, from the solution of equation (3) the number of the television sets that is model p = 12