# Question 1.8: (a) A book is priced at US$20. Calculate the price of the bo...... (a) A book is priced at US$20. Calculate the price of the book in (i) Euros, (ii) British
pounds and (iii) Australian dollars correct to four decimal places.

(b) Convert (i) 500 Australian dollars and (ii) $10 000 Singaporean dollars to pounds sterling. Give all answers correct to four decimal places. Step-by-Step The 'Blue Check Mark' means that this solution was answered by an expert. Learn more on how do we answer questions. The calculations (correct to four decimal places) are carried out as follows: Step 1: State the appropriate rates from Table 1.1. Step 2: Set up the identity: 1 unit of given currency = y units of required currency. Step 3: Multiply both sides by x: x units of given currency = x × (y units of required currency). (a) (i) The price is given in US dollars, the price is required (currency) in Euros, hence Step 1: US$1.3003 = €1        from Table 1.1

Step 2: US$1 = € $\frac{1}{1.3003}$ dividing both sides by 1.3003 Step 3: US$20 = € $\frac{20}{1.3003}$      multiplying both sides by 20

= €15.3811

(a) (ii)
Step 1: From Table 1.1 write down the exchange rates for 1 Euro in both British pounds and US dollars:

$\left. \begin{matrix} US \ 1.3003 = 1 Euro \\ £0.8346 = 1 Euro \end{matrix} \right\} \to US \ 1.3003 = £0.8346$

$1.3003 = £0.8346 since they are each equivalent to 1 Euro The given price is in US dollars, the price is required in British pounds Step 2: US$1 = £1 × $\frac{0.8346}{1.3003}$  dividing both sides of the previous equation by 1.3003 to get rate for $1 in £ Step 3: US$20 = £20 × $\frac{0.8346}{1.3003}$    multiplying both sides by 20

US$20 = £12.8370 (a) (iii) Step 1: From Table 1.1 write down the exchange rates for 1 Euro in Australian dollars and US dollars: $\left. \begin{matrix} US \ 1.3003 = 1 Euro \\ A \ 1.2429 = 1 Euro \end{matrix} \right\} \to US \ 1.3003 = A \ 1.2429$ US$1.3003 = A$1.2429 since they are each equivalent to 1 Euro The given price is US$, the required price (currency) is A$Step 2: US$1 = A$1 × $\frac{1.2429}{1.3003}$ dividing both sides by 1.3003 Step 3: US$20 = A$20 × $\frac{1.2429}{1.3003}$ multiplying both side by 20 = A$19.1171

(b) (i)
Step 1: From Table 1.1 write down the exchange rates for 1 Euro in Australian dollars and pounds sterling:

$\left. \begin{matrix} £0.8346 = 1 Euro \\ A \ 1.2429 = 1 Euro \end{matrix} \right\} \to £0.8346 = A \ 1.2429$

Here we are given A$500 and we require its equivalent in £ sterling A$1.2429 = £0.8346 since they are each equivalent to 1 Euro

Step 2: A$1 = £1 × $\frac{0.8346}{1.2429}$ dividing both sides by 1.2429 to get rate for A$1

Step 3: A$500 = £1 × $\frac{0.8346}{1.2429}$ × 500 multiplying both sides by 500 A$500 = £335.7470

(b) (ii)
Step 1: From Table 1.1 write down the exchange rates for 1 Euro in Singaporean dollars and British pounds:

$\left. \begin{matrix} £0.8346 = 1 Euro \\ S \ 1.6527 = 1 Euro \end{matrix} \right\} \to £0.8346 = S \ 1.6527$

S$1.6527 = £0.8346 since they are each equivalent to 1 Euro Step 2: S$1 = £1 × $\frac{0.8346}{1.6527}$    dividing both sides by 1.6527

Step 3: S$10 000 = £1 × $\frac{0.8346}{1.6527}$ × 10 000 multiplying both sides by 10 000 S$10 000 = £5049.9183

 Table 1.1 Euro exchange rates Currency Rate Currency Rate British pound 0.8346 Canadian dollar 1.3164 US dollar 1.3003 Australian dollar 1.2429 Japanese yen 100.89 Polish zloty 4.2984 Danish krone 7.4352 Hungarian forint 302.8 Brazilian real 2.2923 Hong Kong dollar 10.0912 Swiss franc 1.2065 Singaporean dollar 1.6527 Norwegian krone 7.639 South African rand 10.3843 Malaysian ringgit 4.0147 Indian rupee 65.152

Question: 1.12

## (a) The following equation gives the price (€P) of a concert ticket when there are Qtickets demanded: P = 12 000 − 4Q (i) Make Q the subject of the formula. (ii) Evaluate (1) P when Q = 2980 and (2) Q when the price per ticket P = €40. (b) The sum of the first n terms of an arithmetic series is ...

(a)(i) To make Q the subject of the formula, solve...
Question: 1.13

## USING EXCEL TO PERFORM CALCULATIONS AND PLOT GRAPHS Part-time staff are paid on an hourly basis. The number of hours worked per week with the hourly rate of pay for seven staff are as follows: ...

(a) Enter the data onto the spreadsheet as shown i...
Question: 1.11

## (a) The sum of the first n terms of an arithmetic series is calculated by the formula Sn = n/2(2a + (n – 1)d) Calculate the value of Sn when n = 35, a = 200 and d=−2.5. Note: The subscript in Sn simply indicates that S is the sum of n terms: the sum of 35 terms is written symbolically as S35.(b) In ...

(a) Substitute the values given into the formula [...
Question: 1.10

## (a) Calculate (i) 23% of 1534 (ii) 100% of 1534 (b) A salary of £55 240 is to be increased by 12%. Calculate (i) the increase, (ii) the new salary. (c) In 2013, a holiday apartment is valued at £63 600. This is a drop of 40% on the price paid for the apartment in 2007. Calculate the price paid in ...

(a) In calculations, quoted percentages are always...
Question: 1.9

## Find the range of values for which the following inequalities are true, assuming that x > 0. State the solution in words and indicate the solution on the number line. (a) 10 15 (c) 2x − 6 ≤ 12 − 4x ...

(a) 10 < x − 12 → 10 + 12 < x → 22 < x (o...
Question: 1.7