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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.

Respuesta :

Answer:

(a)

[tex]P=0.7N+2.2[/tex]

(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, [tex]N_1=15,P_1=12.70[/tex]

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

so, [tex]N_2=42,P_2=31.60[/tex]

Firstly, we will find slope

[tex]m=\frac{P_2-P_1}{N_2-N_1}[/tex]

now, we can plug values

[tex]m=\frac{31.60-12.70}{42-15}[/tex]

[tex]m=0.7[/tex]

now, we can use point slope form of line

[tex]P-P_1=m(N-N_1)[/tex]

we can plug value

[tex]P-12.70=0.7(N-15)[/tex]

now, we can solve for P

[tex]P-12.70=0.7N-10.5[/tex]

add both sides by 12.70

[tex]P-12.70+12.70=0.7N-10.5+12.70[/tex]

[tex]P=0.7N+2.2[/tex]

(b)

now, we can plug N=50

[tex]P=0.7\times 50+2.2[/tex]

[tex]P=37.2[/tex]

So,

the price of 50 cloud markers is $37.2