### Solve equations of two unknowns, similar figures

Question Sample Titled 'Solve equations of two unknowns, similar figures'

Let ${A}$ $\text{seconds}$ be the required time of coating metal onto a suitcase of surface area ${P}$ $\text{m}^{{2}}$ . It is given that ${A}$ is the sum of two parts, one part is a constant and the other part varies as ${P}$ . When ${P}={8}$ , ${A}={1250}$ ; when ${P}={14}$ , ${A}={1730}$ .

 (a) Find the required time of coating metal onto a suitcase of surface area of ${18}$ $\text{m}^{{2}}$ . (4 marks) (b) There is a larger suitcase which is similar to the suitcase described in (a). If the volume of the larger suitcase is ${64}$ times that of the suitcase described in (a), find the required time of coating metal onto the larger suitcase. (2 marks)

 (a) Let ${A}={c}+{g}{P}$ , where ${c}$ and ${g}$ are non-zero constants. 1A So, we have ${c}+{8}{g}={1250}$ and ${c}+{14}{g}={1730}$ . 1M Solving, we have ${c}={610}$ and ${g}={80}$ . 1A for both correct The required cost$={610}+{80}{\left({18}\right)}$ $={2050}$ $\text{seconds}$ 1A u-1 for missing unit  (b) By the concept of similar figures, the surface area of the larger suitcase is ${64}^{{\tfrac{{2}}{{3}}}}$ times that of the suitcase decribed in (a) since the volume of the larger suitcase is ${64}$ times that of the suitcase described in (a). 1M The required cost $={610}+{80}{\left({18}\right)}\cdot{64}^{{\tfrac{{2}}{{3}}}}$  $={23650}$ $\text{seconds}$ 1A u-1 for missing unit

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