Frames

A framer is to prepare 23 picture frames. The frame will have dimensions of 30 cm and 42 cm. The strips from which he will make the frames are 3 meters long.

a) How many frames will he make from one strip?
b) How many strips will he need?

Correct answer:

n₁ =  2
n₂ =  12

Step-by-step explanation:

$$\begin{gathered} n=23 \\ a=30\text{cm} \\ b=42\text{cm} \\ L=3\text{m}\to \text{cm}=3\cdot 100\text{cm}=300\text{cm} \\ o=2\cdot (a+b)=2\cdot (30+42)=144\text{cm} \\ {n}_0=L/o=300/144=\frac{25}{12}=2\frac{1}{12}\doteq 2.0833 \\ {n}_1=\lfloor n_0\rfloor =\lfloor 2.0833\rfloor =2 \end{gathered}$$

$$\begin{gathered} n_3=n/n_1=23/2=\frac{23}{2}=11\frac{1}{2}=11.5 \\ {n}_4=n\cdot o/L=23\cdot 144/300=\frac{276}{25}=11\frac{1}{25}=11.04 \\ {n}_4<n_2 \\ {n}_2=\lceil n_4\rceil =\lceil 11.04\rceil =12 \end{gathered}$$

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