At the butcher's

The cold storage room at the butcher's has dimensions 4x3 m, a height of 2.5 m, and a door measuring 90x200 cm. The walls will be tiled up to the ceiling, but before that they need to be treated with two layers of primer and one layer of anti-mould coating. Both products are packaged in buckets with a surface yield of 8 m²/bucket. How many buckets of each product will they need?

Final Answer:

x =  12
y =  6

Step-by-step explanation:

$$\begin{gathered} a=4\text{m} \\ b=3\text{m} \\ c=2.5\text{m} \\ {d}_1=90\text{cm}\to \text{m}=90:100\text{m}=0.9\text{m} \\ {d}_2=200\text{cm}\to \text{m}=200:100\text{m}=2\text{m} \\ h=8{\text{m}}^2\text{/b} \\ {S}_1=d_1\cdot d_2=0.9\cdot 2=\frac{9}{5}=1\frac{4}{5}=1.8{\text{m}}^2 \\ {S}_2=a\cdot b+2\cdot (a+b)\cdot c=4\cdot 3+2\cdot (4+3)\cdot 2.5=47{\text{m}}^2 \\ S=S_2-S_1=47-1.8=\frac{226}{5}=45\frac{1}{5}=45.2{\text{m}}^2 \\ x=\lceil 2\cdot S/h\rceil =\lceil 2\cdot 45.2/8\rceil =12 \end{gathered}$$

$y=\lceil S/h\rceil =\lceil 45.2/8\rceil =6$

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