+10 A saleslady earns a fixed monthly basic salary and a commission that is directly
proportional to the total sales made. For the months of January and February 2014, the
saleslady’s total earnings were Shs 31,200 and Shs 39,000 respectively. Her total sales
for the months of January and February 2014 were Shs 405,000 and Shs 600,000
respectively.
help me find the commission please?
Let her salary be =x
Let the commission rate=y, then we have:
70,200-2x=y*1,005,000. This is a linear Diophantine equation which might have many solutions. But ONE solution that suits your situation is this:
x=15,000 Shs. This is her monthly salary. And,
y=4% This is her commission rate, so that:
4% x 405,000=16,200 Shs + 15,000=31,200 Shs. This is her income for Jan. 2014.
4% x 600,000=24,000 Shs +15,000=39,000 Shs. This is her income for Feb. 2014.
Here is a more elegant solution to this problem:
Let her salary be=x
Solve for x:
(39000-x)/(31200-x) = 40/27
Cross multiply:
27 (39000-x) = 40 (31200-x)
Expand out terms of the left hand side:
1053000-27 x = 40 (31200-x)
Expand out terms of the right hand side:
1053000-27 x = 1248000-40 x
Subtract 1053000-40 x from both sides:
13 x = 195000
Divide both sides by 13:
Answer: | x = 15,000. This is her salary, so that:
31,200 - 15,000=16,200 This is her commission for Jan.2014. Therefore:
16,200/405,000=4% This is her commission rate.
1 mins ago
+129839 Here might be an even easier solutiion :
Let B be her base salary, C be the commission, S be the total sales for a particular month, and E be her earnings for the month
Thus, we have
B + C*(S) = E ...and....we have this system for the two months
B + C*(405000) = 31200 (1)
B + C*(600000) = 39000 (2)
Subtract (1) from (2)
C* (195000) = 7800 divide both sides by 195000
C = 7800/ 195000 = .04 = 4% = her commisiion
