Question

A store sells televisions for $360 and video cassette recorders for $270. At the beginning of the week its entire stock is worth $56,430. During the week it sells three quarters of the televisions and one third of the video cassette recorders for a total of $32,310. How many televisions and video cassette recorders did it have in its stock at the beginning of the week

Answer 1

90 televisions and 89 video cassette recorders

Explanation:

The unit cost of television = $360

The unit cost of video cassette recorder = $270

Let "T" represent the number of televisions and "R" represent the number of recorders, so that we can make representations using equations from the statements.

At the beginning of the week, Total Stock is worth $56,430, where

Total Stock = Total cost of televisions + Total cost of recorders

Total Cost = Unit Cost × Number of items

$56,430 = 360T + 270R This is the first equation

Next, During the week, Number of Sales =
`(3)/(4)` T +
`(1)/(3)` R

Total Sales Price = 360 (
`(3)/(4)` T) + 270 (
`(1)/(3)` R)

$32,310 = 270T + 90R This is the second equation

Solving both equations simultaneously, let us use elimination method which involves equating one of the two terms in both equations. Let us multiply the second equation by 3. This doesn't affect the equation, since we are doing it to all the terms in it.

56,430 = 360T + 270R

32,310 = 270T + 90R × 3

So, we have;

56,430 = 360T + 270R

96,930 = 810T + 270R

Subtracting both equations, we have;

96,930 - 56,430 = 810T - 360T

40,500 = 450T

T =
`(40,500)/(450)` = 90

Since we now have the number of televisions, we can get the number of recorders by putting 90 in any (say, the second) equation.

32,310 = 270 (90) + 90R

32,310 = 24,300 + 90R

32,310 - 24,300 = 90R

8010 = 90R

R =
`(8010)/(90)` = 89

At the beginning of the week, the store had 90 televisions and 89 video cassette recorders

Answer 2

The number of Television at the beginning was 90

The number of video cassette recorders at the beginning was 89

Explanation:

Selling Price of 1 Television =$360.

Selling Price of 1 video cassette recorders for $270.

Let the number of Television at the beginning=x

Let the number of video cassette recorders at the beginning =y

Opening Stock =$56,430.

Therefore:

• 360x+270y=$56,430.

It sells three quarters of the televisions and one third of the video cassette recorders for a total of $32,310.

`(3)/(4)(360)x+(1)/(3)(270)y= \$32,310`

270x+90y=32310

We then solve the two equations to obtain x and y.

• 360x+270y=$56,430. (Multiply by 270)
• 270x+90y=32310 (Multiply by 360)

97200x+72900y=15236100

97200x+32400y=11631600

Subtract

40500y=3604500

y=89

Substitute y=89 into 270x+90y=32310 to obtain x

270x+90(89)=32310

270x=32310-8010=24300

x=90

Therefore:

The number of Television at the beginning was 90

The number of video cassette recorders at the beginning was 89