Henry earns a base salary plus commission. At the end of March he was paid \$2,427 based on his monthly sales of \$15,800. At the end of April he earned \$2,771.50 based on \$21,100 in sales. What was his base salary? You don't have to show your work

The base salary is $1,400

Step-by-step explanation:

Here, we are interested in calculating the base salary.

Now let’s picture his earnings as this, a base salary of let’s say $x and a percentage of y% of total sales as commission.

So let’s move!

For the month of march, his earnings is calculated as follows;

x + (y/100 * 15,800) = 2427

so we have;

x + 158y = 2427 •••••••(i)

For the month of April, we have

x + (y/100 * 21,100) = 2771.5

x + 211y = 2771.5 ••••••(ii)

So we have two equations to solve simultaneously.

We can easily get y by subtracting equation i from ii

That would be ;

(211y-158y) = 2771.5-2427

53y = 344.5

y = 344.5/53

y = 6.5%

So we can now get the base salary by substituting the value of y in any of the equations. Let’s use the first

x + 158(6.5) = 2427

x + 1027 = 2427

x = 2427-1027

x = $1,400

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!