Question

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.

Answer 1

Answer: Cost of 50 markers is $37.2

Equation is

P = 0.7N+2.2

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

Answer 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