The number of 37-inch HDTV's that is expected to be sold in a month is double that of 58-inch HDTV's and 50-inch HDTV's combined.sales of 58-inch HDTV's are expected to be equal. 58-inch HD-TV's sell for $4,800, 50-inch HD-TVs sell for $2000, and 37-inch HDTV's sell for $1800. if total sales of $168,000 are expected this month, how many of each HDTV's should be stocked?

Question

The number of 37-inch HDTV's that is expected to be sold in a month is double that of 58-inch HDTV's and 50-inch HDTV's combined.sales of 58-inch HDTV's are expected to be equal. 58-inch HD-TV's sell for $4,800, 50-inch HD-TVs sell for $2000, and 37-inch HDTV's sell for $1800. if total sales of $168,000 are expected this month, how many of each HDTV's should be stocked?

Answer 1

I ignored this question when you first posted it as "Phil" because the poor punctuation and grammar made it hard to understand.

e.g. "sales of 58-inch HDTV's are expected to be equal."
Equal to what?

Answer 2

Sorry,...... sales of 58-inch and 50 inch are expected to be equal

Answer 3

If the number of 37,50,58-in tv's are x,y,z, then

x = 2(y+z)
y = z
1800x+2000y+4800z = 168000

Now just solve the three equations.

Answer 4

To solve this problem, we need to set up a system of equations based on the information given. Let's represent the number of 37-inch HDTVs as x, the number of 58-inch HDTVs as y, and the number of 50-inch HDTVs as z.

Based on the given information, we can form the following equations:

1) The number of 37-inch HDTVs sold is double that of the combined sales of 58-inch HDTVs and 50-inch HDTVs:
x = 2(y + z)

2) The sales of 58-inch HDTVs are expected to be equal to the sales of 50-inch HDTVs:
4800y = 2000z

3) The total sales for the month are expected to be $168,000:
1800x + 4800y + 2000z = 168000

We now have a system of three equations with three variables. We can solve this system using any method such as substitution or elimination.

Using the second equation, we can express z in terms of y:
z = (4800/2000)y
z = 2.4y

Substituting this value of z in the first equation, we get:
x = 2(y + 2.4y)
x = 2(3.4y)
x = 6.8y

Substituting the values of x and z into the third equation, we have:
1800(6.8y) + 4800y + 2000(2.4y) = 168000

Simplifying the equation, we get:
12240y + 4800y + 4800y = 168000
21840y = 168000
y = 168000/21840
y ≈ 7.69

Since we cannot have fractional quantities of TVs, we need to round y to the nearest whole number. Thus, y = 8.

Substituting this value of y back into the equations, we find:
z = 2.4y ≈ 2.4(8) = 19.2 ≈ 19
x = 6.8y ≈ 6.8(8) = 54.4 ≈ 54

Therefore, you should stock approximately 54 units of 37-inch HDTVs, 8 units of 58-inch HDTVs, and 19 units of 50-inch HDTVs to reach the expected sales of $168,000 for the month.