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 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? (1) The Model P televisions sold for $30 less than the Model Q televisions. (2) Either p = 120 or q = 120.

Answer 1

12 Model P televisions

28 Model Q televisons.

Explanation:

Let
`x` be the number of Model P sold and
`y` the number of Model Q sold. This problem has 4 unknown variables. With the information on the problem you can write some equations:

The total of television sold was 40:

`x+y=40`

The average of the selling price was $141:

`(px+qy)/(40)=141`

The Model P sold for $30 less than the other model:

`p+30=q`

With only three equation, is needed to test them with q=120 and p=120

if
`q=120`

`p+30=q\\p+30=120\\p=120-30=90`

`(90x+120y)/(40)=141\\2.25x+3y=141`

`x+y=40`

Solving the system of equation by the method of elimination (Multiply this equation
`x+y=40` by -3):

`-3x-3y=-120\\2.25x+3y=141\\---------\\-0.75x+0=21\\x=-21/0.75\\x=-28`

Substitute the value of
`x` in one of the equations:

`x+y=40\\-28+y=40\\y=40+28\\y=68\\`

With a
`y` greater than 40 and a negative value of
`x`, this can't be the solution.

if
`p=120`

`p+30=q\\120+30=q\\q=150`

`(120x+150y)/(40)=141\\3x+3.75y=141\\`

Solving the system of equation by the method of elimination (Multiply this equation
`x+y=40` by -3):

`-3x-3y=-120\\3x+3.75y=141\\---------\\0+0.75y=21\\0.75y=21\\y=21/0.75\\y=28`

Substitute the value of
`y` in one of the equations:

`x+y=40\\x+28=40\\x=40-28\\x=12`

They sold 12 Model P televisions and 28 Model Q televisions.