Mr. John is salesman employed to sell television sets on a salary and commission basis. His fixed monthly salary is 500,000. In addition he receives 5% commission on the first 1,000,000 and 12.5% on sales excess of 1,000,000. During the month of march 2013,his total income mounted to 1,400,000. How many television sets did he sell if each costs 1,200,000?
500,000 + .05*1000,000 + .125*(1,200,000x-1,000,000) = 1,400,000
Too many zeros! Let's knock of 000,000 and we have (in millions)
0.5 + .05*1 + .125(1.2x-1) = 1.4
Better check my numbers. I get x = 6.5 ...
To figure out how many television sets Mr. John sold, we can divide his total income by the cost of each television set.
Let's assume:
- x represents the number of television sets sold
- c represents the cost of each television set, which is 1,200,000
The equation we can set up is:
Total income = (Fixed salary) + (Commission on sales)
1,400,000 = 500,000 + (Commission on sales)
Now, let's calculate the commission on sales:
Commission on the first 1,000,000 = 1,000,000 * (5%) = 50,000
Commission on the sales excess of 1,000,000 = (Total income - Commission on the first 1,000,000 - Fixed salary) * (12.5%)
Commission on the sales excess of 1,000,000 = (1,400,000 - 50,000 - 500,000) * (12.5%)
Commission on the sales excess of 1,000,000 = 850,000 * (12.5%) = 106,250
Now, let's substitute these values back into our equation:
1,400,000 = 500,000 + 50,000 + 106,250 + (x * c)
Simplifying the equation by combining like terms:
1,400,000 = 656,250 + (x * c)
Substituting the cost of each television set:
1,400,000 = 656,250 + (x * 1,200,000)
Simplifying further:
1,400,000 - 656,250 = x * 1,200,000
743,750 = x * 1,200,000
To find x, we can divide both sides of the equation by 1,200,000:
x = 743,750 / 1,200,000
Calculating this division:
x ≈ 0.619
Since we are dealing with a number of television sets, we need a whole number. In this case, we can round up to the nearest whole number.
Therefore, Mr. John sold approximately 1 television set since we rounded up to the nearest whole number.