Numbered

The pages of the book are rectangular with sides 15 cm and 12 cm long. Hansel tore out all the pages and lined them up so that they touched on the shorter side. How long was the line, if you know that the pages were numbered starting from number 1 and the sum of the numbers on the last 3 pages was 333? What was the perimeter of the resulting line?

Correct answer:

n =  56
x =  0.15 m
y =  17.04 m

Step-by-step explanation:

(2n-2)+(2n-1)+(2n)=333

(2·n-2)+(2·n-1)+(2·n)=333

6n = 336


n = 336/6 = 56

n = 56

Our simple equation calculator calculates it.

$$\begin{gathered} a=15/100=\frac{3}{20}=0.15 \\ b=12/100=\frac{3}{25}=0.12 \\ x=a\cdot n=0.15\cdot 56=\frac{42}{5}=8.4=0.15\text{m} \end{gathered}$$

$y=2\cdot x+2\cdot b=2\cdot 8.4+2\cdot 0.12=17.04\text{m}$

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