Hair Products A hair product company sells three types of hair products for $30, $20, and $10 per unit. In one

year, the total revenue for the three products was $800,000, which corresponded to the sale of 40,000 units. The
company sold half as many units of the $30 product as units of the $20 product. How many units of each
product were sold?

number of $30 units ---- x

number of $20 units ---- 2x
number of $10 units ---- 40000-x-2x = 40000-3x

30x + 20(2x) + 10(40000-3x) = 800000
30x + 40x + 400000 - 30x = 800000
40x = 400000
x = 10,000

so
10,000 of the $30 units
20,000 of the $20 units
10,000 of the $10

To determine the number of units sold for each hair product, let's assign variables to represent the number of units sold for each product.

Let:
x = number of units sold for the $30 product
y = number of units sold for the $20 product
z = number of units sold for the $10 product

We are given the following information:
1. Total revenue for the three products in one year is $800,000.
2. Total units sold is 40,000.
3. The company sold half as many units of the $30 product as units of the $20 product.

From the given information, we can set up the following equations:

Equation 1: x + y + z = 40,000 (since the total units sold is 40,000)

Equation 2: 30x + 20y + 10z = 800,000 (since the total revenue is $800,000)

Equation 3: x = (1/2) * y (since the company sold half as many units of the $30 product as units of the $20 product)

To solve this system of equations, we can use substitution or elimination method. Let's use substitution:

Substituting Equation 3 into Equation 1:
(1/2) * y + y + z = 40,000
(3/2) * y + z = 40,000

Now we have the following system of equations:
(3/2) * y + z = 40,000
30x + 20y + 10z = 800,000

Solving this system of equations will give us the values of x, y, and z, which represent the number of units sold for each product.