Answer :
Below is a detailed step‐by‐step solution.
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Part 2. Michael’s Spending
Michael starts with a total of \[tex]$250. He spends money on three items:
- Sweets: \$[/tex]25
- Pizza and soda: \[tex]$87.50
- Movie ticket: \$[/tex]50
Step 2.1: Calculate the percentage of his money spent on each item.
1. For sweets, the percentage is
[tex]$$\frac{25}{250} \times 100\% = 10\%.$$[/tex]
2. For pizza and soda, the percentage is
[tex]$$\frac{87.50}{250} \times 100\% = 35\%.$$[/tex]
3. For the movie ticket, the percentage is
[tex]$$\frac{50}{250} \times 100\% = 20\%.$$[/tex]
Step 2.2: Find the fraction of his money that he spends in simplest form.
First, calculate the total amount spent:
[tex]$$25 + 87.50 + 50 = 162.50.$$[/tex]
Then, the fraction of his money spent is
[tex]$$\frac{162.50}{250}.$$[/tex]
To simplify, note that
[tex]$$\frac{162.50}{250} = 0.65 = \frac{65}{100}.$$[/tex]
Dividing numerator and denominator by 5 gives
[tex]$$\frac{65 \div 5}{100 \div 5} = \frac{13}{20}.$$[/tex]
Thus, Michael spends [tex]$\frac{13}{20}$[/tex] of his money.
Step 2.3: Determine the decimal fraction of his money that is left.
The money left after spending is
[tex]$$250 - 162.50 = 87.50.$$[/tex]
The decimal fraction of money left is
[tex]$$\frac{87.50}{250} = 0.35.$$[/tex]
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Part 3. Maths Test Marks
Three students—Ben, Jabu, and Sara—received the following marks:
- Ben: [tex]$86\%$[/tex]
- Jabu: [tex]$\frac{27}{30}$[/tex]
- Sara: [tex]$0.89$[/tex]
Step 3.1: Write Jabu’s mark in its simplest form.
The fraction is
[tex]$$\frac{27}{30}.$$[/tex]
Divide numerator and denominator by 3:
[tex]$$\frac{27 \div 3}{30 \div 3} = \frac{9}{10}.$$[/tex]
Thus, Jabu’s mark in simplest form is [tex]$\frac{9}{10}$[/tex].
Step 3.2: Write all their marks as fractions out of 100.
1. Ben's mark:
[tex]$$86\% = \frac{86}{100}.$$[/tex]
2. Jabu's mark (already simplified) is [tex]$\frac{9}{10}$[/tex] which is equivalent to
[tex]$$\frac{9}{10} = \frac{90}{100}.$$[/tex]
3. Sara's mark:
[tex]$$0.89 = \frac{89}{100}.$$[/tex]
Step 3.3: Write their original marks and percentages in order from highest to lowest.
Convert each mark to a percentage:
- Ben: [tex]$86\%$[/tex]
- Jabu: [tex]$\frac{9}{10} = 90\%$[/tex]
- Sara: [tex]$0.89 = 89\%$[/tex]
Ordering from highest to lowest gives:
[tex]$$90\% \text{ (Jabu)}, \quad 89\% \text{ (Sara)}, \quad 86\% \text{ (Ben)}.$$[/tex]
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Final Answers
2.1
- Sweets: [tex]$10\%$[/tex]
- Pizza and soda: [tex]$35\%$[/tex]
- Movie ticket: [tex]$20\%$[/tex]
2.2 Michael spends [tex]$\frac{13}{20}$[/tex] of his money.
2.3 The decimal fraction of his money that is left is [tex]$0.35$[/tex].
3.1 Jabu's mark in simplest form is [tex]$\frac{9}{10}$[/tex].
3.2 The marks as fractions out of 100:
- Ben: [tex]$\frac{86}{100}$[/tex]
- Jabu: [tex]$\frac{90}{100}$[/tex]
- Sara: [tex]$\frac{89}{100}$[/tex]
3.3 The marks in order from highest to lowest are:
[tex]$$90\%, \; 89\%, \; 86\%.$$[/tex]
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Part 2. Michael’s Spending
Michael starts with a total of \[tex]$250. He spends money on three items:
- Sweets: \$[/tex]25
- Pizza and soda: \[tex]$87.50
- Movie ticket: \$[/tex]50
Step 2.1: Calculate the percentage of his money spent on each item.
1. For sweets, the percentage is
[tex]$$\frac{25}{250} \times 100\% = 10\%.$$[/tex]
2. For pizza and soda, the percentage is
[tex]$$\frac{87.50}{250} \times 100\% = 35\%.$$[/tex]
3. For the movie ticket, the percentage is
[tex]$$\frac{50}{250} \times 100\% = 20\%.$$[/tex]
Step 2.2: Find the fraction of his money that he spends in simplest form.
First, calculate the total amount spent:
[tex]$$25 + 87.50 + 50 = 162.50.$$[/tex]
Then, the fraction of his money spent is
[tex]$$\frac{162.50}{250}.$$[/tex]
To simplify, note that
[tex]$$\frac{162.50}{250} = 0.65 = \frac{65}{100}.$$[/tex]
Dividing numerator and denominator by 5 gives
[tex]$$\frac{65 \div 5}{100 \div 5} = \frac{13}{20}.$$[/tex]
Thus, Michael spends [tex]$\frac{13}{20}$[/tex] of his money.
Step 2.3: Determine the decimal fraction of his money that is left.
The money left after spending is
[tex]$$250 - 162.50 = 87.50.$$[/tex]
The decimal fraction of money left is
[tex]$$\frac{87.50}{250} = 0.35.$$[/tex]
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Part 3. Maths Test Marks
Three students—Ben, Jabu, and Sara—received the following marks:
- Ben: [tex]$86\%$[/tex]
- Jabu: [tex]$\frac{27}{30}$[/tex]
- Sara: [tex]$0.89$[/tex]
Step 3.1: Write Jabu’s mark in its simplest form.
The fraction is
[tex]$$\frac{27}{30}.$$[/tex]
Divide numerator and denominator by 3:
[tex]$$\frac{27 \div 3}{30 \div 3} = \frac{9}{10}.$$[/tex]
Thus, Jabu’s mark in simplest form is [tex]$\frac{9}{10}$[/tex].
Step 3.2: Write all their marks as fractions out of 100.
1. Ben's mark:
[tex]$$86\% = \frac{86}{100}.$$[/tex]
2. Jabu's mark (already simplified) is [tex]$\frac{9}{10}$[/tex] which is equivalent to
[tex]$$\frac{9}{10} = \frac{90}{100}.$$[/tex]
3. Sara's mark:
[tex]$$0.89 = \frac{89}{100}.$$[/tex]
Step 3.3: Write their original marks and percentages in order from highest to lowest.
Convert each mark to a percentage:
- Ben: [tex]$86\%$[/tex]
- Jabu: [tex]$\frac{9}{10} = 90\%$[/tex]
- Sara: [tex]$0.89 = 89\%$[/tex]
Ordering from highest to lowest gives:
[tex]$$90\% \text{ (Jabu)}, \quad 89\% \text{ (Sara)}, \quad 86\% \text{ (Ben)}.$$[/tex]
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Final Answers
2.1
- Sweets: [tex]$10\%$[/tex]
- Pizza and soda: [tex]$35\%$[/tex]
- Movie ticket: [tex]$20\%$[/tex]
2.2 Michael spends [tex]$\frac{13}{20}$[/tex] of his money.
2.3 The decimal fraction of his money that is left is [tex]$0.35$[/tex].
3.1 Jabu's mark in simplest form is [tex]$\frac{9}{10}$[/tex].
3.2 The marks as fractions out of 100:
- Ben: [tex]$\frac{86}{100}$[/tex]
- Jabu: [tex]$\frac{90}{100}$[/tex]
- Sara: [tex]$\frac{89}{100}$[/tex]
3.3 The marks in order from highest to lowest are:
[tex]$$90\%, \; 89\%, \; 86\%.$$[/tex]
