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Financial Maths, STD2 EQ-Bank 24

Yuki works as a musician and receives royalties from streaming services. A spreadsheet is used to calculate her quarterly royalty earnings.

Total royalty earnings = Number of streams \(\times\) Royalty rate per stream

A spreadsheet showing Yuki's quarterly royalty earnings is shown.

  

 

In the following quarter, Yuki's total royalty earnings were $4200. The royalty rate per stream remained at $0.004. Calculate the number of streams Yuki received that quarter.   (2 marks)

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\(1\,050\,000\)

Show Worked Solution

\(\text{Total royalty earnings (B8)} = $4200\)

\(\text{Royalty rate per stream (B5)}=$0.004\)

\(\text{Let the number of streams (B4)}=N\)

\(\text{Total royalty earnings} = \text{Number of streams} \times\text{Royalty rate per stream}\)

\(\text{B8}\) \(=\text{B4}^*\text{B5}\)
\(4200\) \(=N\times 0.004\)
\(N\) \(=\dfrac{4200}{0.004}\)
  \(=1\,050\,000\)

\(\text{Yuki had 1 050 000 streams in the next quarter}\)

Financial Maths, STD2 EQ-Bank 21

Liam works in a factory assembling electronic components and is paid on a piecework basis. A spreadsheet is used to calculate his weekly earnings.

Weekly earnings = Number of units completed \(\times\) Rate per unit

A spreadsheet showing Liam's earnings for one week is shown.
  

  1. Write down the formula used in cell B8, using appropriate grid references.   (1 mark)

  2. In the following week, Liam earned $2036.25. The rate per unit remained at $3.75. Calculate the number of units Liam completed that week.   (2 marks)

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a.   \(=\text{B4}^*\text{B5}\)

b.    \(\text{Number of units completed}=543\)

Show Worked Solution

a.   \(\text{Weekly earnings} = \text{Number of units completed} \times \text{Rate per unit}\)

\(\text{Formula:}\ =\text{B4}^*\text{B5}\)
 

b.   \(\text{Weekly earnings} = \text{Number of units completed} \times \text{Rate per unit}\)

\(\text{Let the Weekly earnings}=E\)

\(2036.25\) \(=E\times 3.75 \)
\(E\) \(=\dfrac{2036.25}{3.75}=543\)

Financial Maths, STD2 EQ-Bank 19

Maria works as a freelance writer and earns income through royalties. A spreadsheet is used to calculate her monthly royalty earnings.

Royalties = Number of books sold \( \times \) Royalty rate per book

A spreadsheet showing Maria's royalty earnings is shown.
  

  1. Write down the formula used in cell B8, using appropriate grid references.   (1 mark)

  2. In April, Maria earned total royalty earnings of $8960. Her royalty rate remained at $2.85 per book. How many books did Maria sell in April?   (2 marks)

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a.   \(=\text{B4}^*\text{B5}\)

b.    \(\text{Number of books}=3144\)

Show Worked Solution

a.   \(\text{Total royalty earnings} = \text{Number of books sold} \times \text{Royalty rate per book}\)

\(\text{Formula:}\ =\text{B4}^*\text{B5}\)
 

b.   \(\text{Total royalty earnings} = \text{Number of books sold} \times \text{Royalty rate per book}\)

\(\text{Let the Number of books sold}=N\)

\(8960.40\) \(=N\times 2.85 \)
\(N\) \(=\dfrac{8960.40}{2.85}=3144\)

Financial Maths, STD2 EQ-Bank 18

Michael is a children's book author. His publisher printed 25000 copies of his new book and after 6 months there are 9200 copies left in stock. Michael receives 12% of the retail price as royalties.

  1. How many copies of Michael's book were sold?   (1 mark)
  2. Calculate Michael's royalty payment if the retail price is $19.95.   (2 marks)
  3. The publisher decides to sell the remaining stock at a reduced price of $15.00 per book. Calculate Michael's total royalty payment if all the remaining books are sold at this price.   (2 marks)
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a.    \(15\,800\ \text{copies}\)

b.    \($37\,825.20\)

c.    \($54\,385.20\)

Show Worked Solution

a.    \(\text{Copies sold}\ =25\,000-9200\ =15\,800\ \text{copies}\)

b.    \(\text{Total sales}\ =15\,800\times 19.95=$315\,210\)

\(\text{Royalty payment}\) \(=12\% \times 315\,210\)
  \(= 0.12\times 315\,210\)
  \(=$37\,825.20\)

 

c.    \(\text{Sales from remaining books}\ =9200\times 15.00\ =$138\,000\)

\(\text{Total royalty on remaining books}\ =0.12\times 138\,000=$16\,560\)

\(\text{Total royalty when all books sold}\ = 37\,825.20 + 16\,560\ =$54\,385.20\)

\(\therefore\ \text{Michael’s total royalty payment is }$54\,385.20\)

Financial Maths, STD2 EQ-Bank 24

Sophie is a songwriter and receives a royalty of 9.5% on the sales of her music album.

Calculate Sophie's royalty payment if 15600 albums were sold at $22.95 each.   (2 marks)

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\($34\,011.90\)

Show Worked Solution

\(\text{Total sales}\ =15\,600 \times 22.95\ =$358\,020\)

\(\text{Royalty payment}\) \(=9.5\% \times 358\,020\)
  \(= 0.095\times 358\,020\)
  \(=$34\,011.90\)

 
\(\therefore\ \text{Sophie’s royalty payment is }$34\,011.90\)

Financial Maths, STD2 EQ-Bank 10 MC

An author receives a 15% royalty on book sales. In the first quarter, 12000 copies were printed and 8400 copies were sold at $32.50 each.

What is the author's royalty payment for the first quarter?

  1. $40 950
  2. $41 400
  3. $58 500
  4. $59 800
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\(A\)

Show Worked Solution

\(\text{Copies sold} = 8400\)

\(\text{Total sales}\ =8400 \times 32.50\ =$273\,000\)

\(\text{Royalty payment}=15\% \times 273\,000= 0.15\times 273\,000=$40\,950\)

\(\Rightarrow A\)

Financial Maths, STD2 EQ-Bank 5 MC

A musician receives a royalty of 8% on album sales.

If 3500 albums were sold at $18.00 each, what is the musician's royalty payment?

  1. $4320
  2. $5040
  3. $5600
  4. $6300
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\(B\)

Show Worked Solution

\(\text{Total sales}\ =3500 \times 18.00\ =$63\,000\)

\(\text{Royalty payment}\) \(=8\% \times 63\,000\)
  \(= 0.08\times 63\,000=$5040\)

\(\Rightarrow B\)

Financial Maths, STD2 EQ-Bank 23

Jessica works in a shoe factory and is paid $5.40 for each pair of shoes she completes. Last week she worked 9 hours per day for 4 days and completed 180 pairs of shoes.

Calculate her hourly rate of pay.   (2 marks)

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\($27.00\text{/hour}\)

Show Worked Solution

\(\text{Total earnings}=5.40\times 180= $972\)

\(\text{Total hours worked}=9 \times 4= 36\ \text{hours}\)

\(\text{Hourly rate}=\dfrac{972}{36}=$27.00\text{/hour}\)

\(\therefore\ \text{Jessica’s hourly rate is }$27.00\)

Financial Maths, STD2 EQ-Bank 15 MC

A garment worker is paid $4.20 for each shirt she completes. In a particular week she worked 8 hours per day for 5 days and earned $1176.

How many shirts per hour did she complete on average?

  1. 5
  2. 6
  3. 7
  4. 8
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\(C\)

Show Worked Solution

\(\text{Number of shirts}=\dfrac{1176}{4.20}= 280\ \text{shirts}\)

\(\text{Total hours worked}=8 \times 5= 40\ \text{hours}\)

\(\text{Shirts per hour}=\dfrac{280}{40}=7\)

\(\Rightarrow C\)

Financial Maths, STD2 EQ-Bank 4 MC

Sam is paid $2.50 for each toy he assembles in a factory. In one week he worked 35 hours and assembled 168 toys.

What is Sam's hourly rate of pay?

  1. $10.00
  2. $12.00
  3. $14.00
  4. $16.00
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\(B\)

Show Worked Solution

\(\text{Total earnings}=2.50 \times 168= $420 \)

\(\text{Hourly rate}=\dfrac{\text{Total earnings}}{\text{Hours worked}}= \dfrac{420}{35}=$12.00\)

\(\Rightarrow B\)

Financial Maths, STD2 EQ-Bank 3 MC

Maria works in a textile factory and is paid $1.20 for each scarf she completes. Last week Maria earned $456.

How many scarves did she complete?

  1. 360
  2. 380
  3. 400
  4. 420
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\(B\)

Show Worked Solution
\(\text{Number of scarves}\) \(=\dfrac{\text{Total earnings}}{\text{Payment per scarf}}\)
  \(= \dfrac{456}{1.20} =380\)

\(\Rightarrow A\)