2. Two teachers, Mr. Donahue and Mrs. Ortiz, decide to buy mechanical pencils and rulers for their classrooms. Mrs. Ortiz buys 50 mechanical pencils and 30 rulers for $55. Mr. Donahue buys 30 of each for $45. What was the price per mechanical pencil? What was the price per ruler? a. Fill in the equation for the cost of Mrs. Ortiz's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.

= x + y

b. Fill in the equation for the cost of Mr. Donahue's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.

= x + y

c. Circle the best method for solving the system:

Graphing Substitution Elimination

d. Solve the system using the method you chose.

A mechanical pencil costs and a ruler costs .

e. Check your

Step-by-step explanation:

a. Fill in the equation for the cost of Mrs. Ortiz's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.

__$55__ = __50__ x + __30_ y

b. Fill in the equation for the cost of Mr. Donahue's purchase. Let x represent the cost of a pencil and y represent the cost of a ruler.

__$45__ = __30__ x + __30__ y

c. Circle the best method for solving the system:

Elimination

d. Solve the system using the method you chose.

  55 =50x+30y

  -1(45) =(30x+30y)-1     =     -45=-30x-30y

    55 =50x+30y

+  -45=-30x-30y

   10=20x

(1/20)10=20x(1/20)

0.50=x

3(55) =(50x+30y )3      =     165=150x+90y

-5(45) =(30x+30y)-5     =   -225=-150x-150y

     165 =150x+90y

+  -225=-150x-150y

           -60=-60y

(1/-60)-60=-60y(1/-60)

             1=y

A mechanical pencil costs _$0.50__ and a ruler costs __$1.00__.

e. Check your

$55=50x+30y                                $45=30x+30y

$55=50(0.5)+30(1)                         $45=30(0.5)+30(1)

$55=25+30                                    $45=15+30

$55=$55                                         $45=$45

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional