The price of a box of 15 cloud markers is $12.70. the price of a box of 42 cloud markers is $31.60. all prices are without tax, and the price of the packaging is the same for any size. how much would 50 cloud markers in a box cost? write an equation which will tell the price p for the number n markers in the box.

(a)

(b)

the price of 50 cloud markers is $37.2

Step-by-step explanation:

(a)

Let's assume

price is P

number of markers is N

We are given

The price of a box of 15 cloud markers is $12.70

so,

The price of a box of 42 cloud markers is $31.60

so,

Firstly, we will find slope

now, we can plug values

now, we can use point slope form of line

we can plug value

now, we can solve for P

add both sides by 12.70

(b)

now, we can plug N=50

So,

the price of 50 cloud markers is $37.2

Cost of 50 markers is $37.2

               Equation is

                  P = 0.7N+2.2

Step-by-step explanation:

Let the cost Packaging be 'c'  and x be the cost of one marker and P be the total cost

So the equation for the  total cost is

                        P = Nx +c

then cost of 15 markers is 15x +c = $12.70 equation (1)

similarly cost of 42 markers is 42N+c =$ 31.60 equation (2)

         Subtracting equation 2 from equation 1 ,we get

42N+c = 31.60

-15x -c = 12.70

27x =18.9

x = 0.7

Plugging x = 0.7 in equation 1

15(0.7) + c = 12.7

10.5 +c = 12.7

  c = 2.2

Therefore cost equation is

P = 0.7N +2.2

Cost of 50 markers will be

P = 0.7(50) +2.2

  = 35.0 + 2.2

 =$ 37.2

 

Here, The price of one box having N markers = Price of N markers + packaging charge

Let M be the price of one Marker and P' be the price of packaging of one box which is same for any size.

Since, The price of a box of 15 cloud markers is $12.70.

That is , 15 M + P' = 12.70 (1)

Also,  The price of a box of 42 cloud markers is $31.60,

That is, 42 M + P' = 31.60 (2),

Equation (2) - Equation (1),

27 M = 18.90,

⇒ M = 0.7

By putting the value of P in equation (1),

We get,

10.5 + P' = 12.70 ⇒ P' = 2.2,

Thus, the price of one marker, M = 0.7

And, the price of packaging one box, P' = 2.2

Thus, the price of a box of 50 marker = 50 × M + P' = 50×0.7 + 2.2 = 35 + 2.2 = $ 37.2

And, the equation that shows the price(P) of a box of N markers,

P = 0.7 N + 2.2

P = 0.7N + 2.20

50 markers cost $37.20

Step-by-step explanation:

We know a box of 15 costs $12.70 and a box of 42 costs $31.60. Since the price of packaging is the same no matter the size, the price will go up at a constant rate. To find this rate, subtract the price 31.60-12.70 = 18.90 Divide it by the difference in number of markers in a box 42-15 = 27. So 18.9/27 = 0.7. This means for every marker added the price increases by $0.70. This is a linear relationship. Use the point slope form to write the equation.

Here y is price P and x is N for number of markers.

P = 0.7N+2.20

To find the price for 50 markers, substitute N=50.

P = 0.7(50)+2.20

P= 37.20