Mark wants to start saving money. He
makes an annual net income of $45,000
at his computer technician job.
misc. 7%
debt 5%
housing 30%
gifts & entertainment 12%
clothes 5%
Spending Guidelines
(% of net incomes)
1: What is his net monthly pay?
Monthly Expenditures
Rent: $850
Food: $300
Car insurance + gas: $190
Entertainment: $760
Clothes: $150

2: What approximate percentage of his net
monthly pay is each expenditure listed above?
savings: 10%
transportation: 11%
food: 20%
3: Where would you suggest he cut costs to
be able to save more money each month?
2a: What percentage of his net monthly pay is his rent payment?

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!

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