Read the problems and and write the word that indicates an equation or inequality and decide whether an equation or inequality is indicated Brett has a $30 online gift certificate. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2. How many books can he afford without spending more than his gift certificate amount? Word/phrase? Equation/Inequality

Word/phrase : Equation

Equation:4x + 2 = $30

He can afford to buy 7 books without spending more than his gift certificate amount

Step-by-step explanation:

Step 1

We find the equation

Brett has a $30 online gift certificate. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2.

Hence,

$4 × x + $2 = $30

Where x = number of books that he can buy

4x + 2 = $30

Step 2

We solve for x

4x + 2 = 30

4x = 30 - 2

4x = 28

x = 28/4

x = 7

Hence, Brett can buy 7 books

Equation: 4x + 2 = $30

Word/phrase : Equation

He can afford to buy 7 books without spending more than his gift certificate amount

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!