Tablecloths

The restaurant has sixty-two square tablecloths with a side length of 150 cm and 36 rectangular tablecloths with dimensions of 140 cm and 160 cm.

A) How many meters of hemming ribbon will be needed if we add 50 cm to each tablecloth?
B) The ribbon sale in packages of 25 meters. How many packages must a company order?

Correct answer:

x =  637 m
n =  26

Step-by-step explanation:

$$\begin{gathered} a_1=150\text{ cm}\to \text{ m}=150\mathrm{/}100\text{ m}=1.5\text{ m } \\ {n}_1=62 \\ {n}_2=36 \\ {a}_2=140\text{ cm}\to \text{ m}=140\mathrm{/}100\text{ m}=1.4\text{ m } \\ {b}_2=160\text{ cm}\to \text{ m}=160\mathrm{/}100\text{ m}=1.6\text{ m } \\ u=50\text{ cm}\to \text{ m}=50\mathrm{/}100\text{ m}=0.5\text{ m } \\ x=(n_1+n_2)\cdot u+n_1\cdot 4\cdot a_1+n_2\cdot 2\cdot (a_2+b_2)=(62+36)\cdot 0.5+62\cdot 4\cdot 1.5+36\cdot 2\cdot (1.4+1.6)=637\text{ m} \end{gathered}$$

$$\begin{gathered} n_3=x\mathrm{/}25=637\mathrm{/}25={\displaystyle \frac{637}{25}}=25\frac{12}{25}=25.48 \\ n=\lceil n_3\rceil =\lceil 25.48\rceil =26 \end{gathered}$$

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