Assignment1 – BD309_2526 – Steven Harazaki Lase – 2381477560

PERTANYAAN :

1.A law firm seeks to recruit top-quality experienced lawyers. The total package offered is

the sum of three separate components: a basic salary which is 1.2 times the candidate’s

current salary together with an additional $3000 for each year worked as a qualified

lawyer and an extra $1000 for every year that they are over the age of 21.

Work out a formula that could be used to calculate the total salary, S, offered to

someone who is A years of age, has E years of relevant experience and who currently

earns $N. Hence work out the salary offered to someone who is 30 years old with five

years’ experience and who currently earns $150 000.

 

2.Write down a formula for each situation:

a. A plumber has a fixed call-out charge of $80 and has an hourly rate of $60. Work

out the total charge, C, for a job that takes L hours in which the cost of materials

and parts is $K.

b.An airport currency exchange booth charges a fixed fee of $10 on all transactions

and offers  an exchange rate of 1 dollar to 0.8 euros. Work out the total charge, C,

(in $) for buying x euros.

c. A firm provides 5 hours of in-house training for each of its semi-skilled workers and

10 hours of training for each of its skilled workers. Work out the total number of

hours, H, if the firm employs a semi-skilled and b skilled workers.

d. A car hire company charges $C a day together with an additional $c per mile. Work

out the total charge, $X, for hiring a car for d days and travelling m miles during

that time.

Without using a calculator, evaluate

(a) 10 × (−2) (b) (−1) × (−3) (c) (−8) ÷ 2 (d) (−5) ÷ (−5)

(e) 24 ÷ (−2) (f) (−10) × (−5) (f) (−6) × 5 × (−1)

 

3.Without using a calculator, evaluate

(a) 5 − 6 (b) −1 − 2 (c) 6 − 17 (d) −7 + 23

(e) −7 − (−6) (f) −4 − 9 (g) 7 − (−4) (h) −9 − (−9)

(i) 12 − 43 ( j) 2 + 6 − 10

 

4.Without using a calculator, evaluate

(a) 5 × 2 − 13 (b) 5 × (1 − 4)

(c) 1 − 6 × 7 (d) −5 + 6 ÷ 3 (e) 2 × (−3)2 (f) −10 + 22

(g) (−2)2 − 5 × 6 + 1 ( j)

 

5.Simplify each of the following algebraic expressions:

(a) 2 × P × Q (b) I × 8 (c) 3 × x × y

(d) 4 × q × w × z (e) b × b (f) k × 3 × k

 

STATUS :

KETERANGAN :

BUKTI :

1.

Step 1: Define the formula

We are told:

• Basic salary = $1.2\times N$

• Experience bonus = $3000\times E$

• Age bonus = $1000\times (A-21)$ (only counts years over age 21)

So, the total salary $S$ is:

$$S=1.2N+3000E+1000(A-21)$$

Step 2: Substitute the values given

• $A=30$

• $E=5$

• $N=150,000$

$$S=1.2(150,000)+3000(5)+1000(30-21)$$

Step 3: Calculate step by step

1. Basic salary:

$$1.2\times 150,000=180,000$$

2. Experience bonus:

$$3000\times 5=15,000$$

3. Age bonus:

$$30-21=9\Rightarrow 1000\times 9=9,000$$

Step 4: Add them up

$$S=180,000+15,000+9,000=204,000$$

✅ Final Formula:

S=1.2N+3000E+1000(A−21)\boxed{S = 1.2N + 3000E + 1000(A – 21)}S=1.2N+3000E+1000(A−21)​

✅ Salary Offered:

S=$204,000\boxed{S = \$204,000}S=$204,000

 

2.​

(a) Plumber: fixed call-out $80, hourly rate $60, job takes $L$ hours, materials cost $$K$.

C=80+60L+K\boxed{C = 80 + 60L + K}C=80+60L+K​

(b) Currency booth: fixed fee $10, exchange rate $1\$=0.8\text{euros}$. To buy $x$ euros you need x0.8=1.25x\dfrac{x}{0.8}=1.25x0.8x​=1.25x dollars plus the fee:

C=10+x0.8=10+1.25x\boxed{C = 10 + \dfrac{x}{0.8} = 10 + 1.25x}C=10+0.8x​=10+1.25x​

(c) Training hours: 5 hours per semi-skilled worker, 10 hours per skilled worker. If firm employs $a$ semi-skilled and $b$ skilled workers:

H=5a+10b\boxed{H = 5a + 10b}H=5a+10b​

(d) Car hire: $$C$ per day and $$c$ per mile. For $d$ days and $m$ miles:

X=Cd+cm\boxed{X = Cd + cm}X=Cd+cm​

Without calculator — evaluate:

Work carefully, step by step:

(a) $10\times (-2)=-20$
(b) $(-1)\times (-3)=+3$
(c) $(-8)÷2=-4$
(d) $(-5)÷(-5)=+1$
(e) $24÷(-2)=-12$
(f) $(-10)\times (-5)=+50$

You listed (f) twice; I’ll label the last one as (g):

(g) $(-6)\times 5\times (-1)$. First $(-6)\times 5=-30$, then $-30\times (-1)=+30$.

So final results:
(a) $-20$, (b) $3$, (c) $-4$, (d) $1$, (e) $-12$, (f) $50$, (g) $30$

3.

(a) $5-6=-1$

(b) $-1-2=-3$

(c) $6-17=-11$

(d) $-7+23=16$

(e) $-7-(-6)=-7+6=-1$

(f) $-4-9=-13$

(g) $7-(-4)=7+4=11$

(h) $-9-(-9)=-9+9=0$

(i) $12-43=-31$

(j) $2+6-10=8-10=-2$

4.

(a) 5 × 2 − 13

1. $5\times 2=10$

2. $10-13=-3$
   ✅ Jawaban: -3

(b) 5 × (1 − 4)

1. Hitung dalam kurung: $1-4=-3$

2. $5\times -3=-15$
   ✅ Jawaban: -15

(c) 1 − 6 × 7

1. Kali dulu: $6\times 7=42$

2. $1-42=-41$
   ✅ Jawaban: -41

(d) −5 + 6 ÷ 3

1. Bagi dulu: $6÷3=2$

2. $-5+2=-3$
   ✅ Jawaban: -3

(e) 2 × (−3)²

1. Kuadrat dulu: (−3)2=9(−3)² = 9(−3)2=9

2. $2\times 9=18$
   ✅ Jawaban: 18

(f) −10 + 22
$-10+22=12$
✅ Jawaban: 12

(g) (−2)² − 5 × 6 + 1

1. Kuadrat dulu: (−2)2=4(−2)² = 4(−2)2=4

2. Kali: $5\times 6=30$

3. $4-30+1=(4+1)-30=5-30=-25$
   ✅ Jawaban: -25

 

5.

(a) 2 × P × Q
Tidak ada angka atau variabel yang sama untuk dikalikan, jadi kita cukup menuliskannya berurutan:
✅ Jawaban: 2PQ

(b) I × 8
Urutkan angka di depan huruf:
✅ Jawaban: 8I

(c) 3 × x × y
Gabungkan:
✅ Jawaban: 3xy

(d) 4 × q × w × z
Gabungkan:
✅ Jawaban: 4qwz

(e) b × b
Variabel sama → dijadikan pangkat:
✅ Jawaban: b²

(f) k × 3 × k

1. Gabungkan angka dulu: $3$

2. k×k=k2k × k = k²k×k=k2
   ✅ Jawaban: 3k²