with summer appraching,t he number of air conditioners sold is expected to be double hat of stoves and refrigerators combined. stove sell for $350, refrigerators for $450, and air conditoners for $500, and sales of $56,000 are expected. If stoves and refrigerators sell in equal numbers, how many of each appliance should be stocked?
looks like we have to solve
350x + 450x + 500(4x) = 56000
To determine the number of each appliance that should be stocked, we need to set up a system of equations based on the given information.
Let's assume the number of stoves and refrigerators sold is represented by 'x', and the number of air conditioners sold is represented by 'y'.
1) According to the given information, the number of air conditioners sold is expected to be double that of stoves and refrigerators combined. Mathematically, we can express this as:
y = 2(x + x) = 2(2x) = 4x
2) The cost of stoves is $350 per unit, refrigerators are $450 per unit, and air conditioners are $500 per unit. We are given that the total expected sales amount to $56,000. So, we can set up the second equation based on the costs and quantities:
350x + 450x + 500y = 56000
Now we have a system of two equations:
4x = y ...(Equation 1)
350x + 450x + 500y = 56000 ...(Equation 2)
To solve this system of equations, we can use substitution or elimination method. Let's use substitution method to find the values of x and y.
From Equation 1, we can express y in terms of x:
y = 4x
Substituting this into Equation 2:
350x + 450x + 500(4x) = 56000
350x + 450x + 2000x = 56000
(350 + 450 + 2000)x = 56000
2800x = 56000
x = 56000 / 2800
x = 20
Now, substitute the value of x back into Equation 1:
y = 4x
y = 4(20)
y = 80
Therefore, the number of stoves should be 20, the number of refrigerators should be 20, and the number of air conditioners should be 80 in order to meet the expected sales of $56,000.