### 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

# 專業備試計劃

DSE Preparation Plan

Level 4+ 保證及 5** 獎賞

### 常見問題

ePractice 是甚麼？

ePractice 是一個專為中四至中六而設的應用程式，旨為協助學生高效地預備 DSE 數學（必修部分）考試。ePractice 是網站應用程式，因此無論使用任何裝置、平台，都可以在瀏覽器開啟使用。更多詳情請到簡介頁面。

### 簡介

ePractice 可以取代傳統補習嗎？

ePractice 是甚麼？

ePractice 是一個專為中四至中六而設的應用程式，旨為協助學生高效地預備 DSE 數學（必修部分）考試。ePractice 是網站應用程式，因此無論使用任何裝置、平台，都可以在瀏覽器開啟使用。更多詳情請到簡介頁面。

### 帳戶

「體驗帳戶」可以使用多久？

「體驗帳戶」不會過期，但用戶只能做 30 條題目，而且觀看少部分的知識內容。如希望無限量使用 ePractice 的所有練習服務及內容，請成為我們的會員！

### 有關繳款

ePractice 提供對所有會員服務購買的 14 天無條件退款保證（恕不適用於服務期少於兩個月的計劃）。請聯絡我們並提供相關訂單編號以進行退款。如您透過信用卡付款，款項將退回至您的信用卡。如使用其他付款方式，請提供您的銀行帳號、FPS ID 或 PayMe ID 以便進行退款轉帳。

Initiating...

HKDSE 數學試題練習平台