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?
If the number of 37,50,58-in tv's are x,y,z, then
x = 2(y+z)
z = ? (which are equal?)
1800x+2000y+4800z = 168000
Fix the second condition, and then solve the three equations.
To solve this problem, we can set up a system of equations based on the given information.
Let's represent the number of 58-inch HDTVs as "x", the number of 50-inch HDTVs as "y", and the number of 37-inch HDTVs as "z".
From the information provided, we know that the number of 37-inch HDTVs sold is double the sum of the 58-inch and 50-inch HDTVs sold. So we can write the equation:
z = 2(x + y)
We also know that the sales of 58-inch HDTVs are expected to be equal to x. So the sales revenue from 58-inch HDTVs is given by:
Revenue from 58-inch HDTVs = x * $4800
Similarly, we can find the revenue from 50-inch and 37-inch HDTVs:
Revenue from 50-inch HDTVs = y * $2000
Revenue from 37-inch HDTVs = z * $1800
The total sales revenue for the month is expected to be $168,000. So we can set up another equation:
Total revenue = Revenue from 58-inch HDTVs + Revenue from 50-inch HDTVs + Revenue from 37-inch HDTVs
$168,000 = (x * $4800) + (y * $2000) + (z * $1800)
Now we have two equations: z = 2(x + y) and $168,000 = (x * $4800) + (y * $2000) + (z * $1800).
We can now solve these two equations to find the values of x, y, and z.
First, we rearrange the equation z = 2(x + y) to express one variable in terms of the other:
z = 2x + 2y
Next, we substitute the expression for z in the revenue equation:
$168,000 = (x * $4800) + (y * $2000) + ((2x + 2y) * $1800)
Simplifying this equation will give us the values of x, y, and z, which represent the number of each type of HDTV that should be stocked.