91267 – Worked Solutions - 2025
QUESTION THREE
2.12 (AS 91267) – 2025 Answers
Quite often, there are different ways to solve a Mathematics problem.
These solutions/strategies show one possible way to solve them.
Question 3(a) i
The cafe records the following information from customers, based on the most popular coffee selections.
(i) What percentage of customers ordered a cappuccino?
Question 3(a) i
The cafe records the following information from customers, based on the most popular coffee selections.
(i) What percentage of customers ordered a cappuccino?
Question 3(a) i
The cafe records the following information from customers, based on the most popular coffee selections.
(i) What percentage of customers ordered a cappuccino?
Question 3(a) ii
The cafe records the following information from customers, based on the most popular coffee selections.
(ii) What is the probability that a randomly selected teenager orders a latte?
Question 3(a) ii
The cafe records the following information from customers, based on the most popular coffee selections.
(ii) What is the probability that a randomly selected teenager orders a latte?
Question 3(a) ii
The cafe records the following information from customers, based on the most popular coffee selections.
(ii) What is the probability that a randomly selected teenager orders a latte?
Probabilities can be written as a fraction, decimal or percentage.
Question 3(a) iii
The cafe records the following information from customers, based on the most popular coffee selections.
(iii) What is the probability that a randomly selected customer is either an adult or a cappuccino drinker?
Question 3(a) iii
The cafe records the following information from customers, based on the most popular coffee selections.
(iii) What is the probability that a randomly selected customer is either an adult or a cappuccino drinker?
Question 3(a) iii
The cafe records the following information from customers, based on the most popular coffee selections.
(iii) What is the probability that a randomly selected customer is either an adult or a cappuccino drinker?
Probabilities can be written as a fraction, decimal or percentage.
Question 3(b) i
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(i) Explain why the owner believes this.
Question 3(b) i
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(i) Explain why the owner believes this.
Question 3(b) i
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(i) Explain why the owner believes this.
The owner has simply looked at the number of adults that ordered a Mocha (150) and compared this with the number of teenagers that ordered a Mocha (76).
150 is almost double 76, hence the owner has made the assumption it is twice as likely an adult orders a Mocha compared to a teenager.
Question 3(b) ii
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(ii) Show with appropriate calculations how the manager can prove to the owner that he is wrong.
Question 3(b) ii
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(ii) Show with appropriate calculations how the manager can prove to the owner that he is wrong.
Question 3(b) ii
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(ii) Show with appropriate calculations how the manager can prove to the owner that he is wrong.
We need to use relative risk and compare the proportion of adults and teenagers buying a Mocha, based on how many adults and teenagers were at the café.
Question 3(b) ii
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(ii) Show with appropriate calculations how the manager can prove to the owner that he is wrong.
We need to use relative risk and compare the proportion of adults and teenagers buying a Mocha, based on how many adults and teenagers were at the café.
Question 3(b) ii
From the data, the owner believes that it is twice as likely for an adult than for a teenager to order a mocha. His manager thinks that he is wrong.
(ii) Show with appropriate calculations how the manager can prove to the owner that he is wrong.
We need to use relative risk and compare the proportion of adults and teenagers buying a Mocha, based on how many adults and teenagers were at the café.
Question 3(b) ii
We need to use relative risk and compare the proportion of adults and teenagers buying a Mocha, based on how many adults and teenagers were at the café.
The relative risk of adults buying a Mocha compared to teenagers is only 1.49. This means that adults were 1.49 times more likely to buy a Mocha than teenagers. In Mathematics, we cannot round this to 2 and say it is twice as likely, so the owner is unfortunately incorrect with their thinking.
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
347 – 267 = 80
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
390 – 267 = 123
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
123 + 130 = 253
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
80 + 130 = 210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Two quick checks:
390 + 210 = 600
347+253 = 600
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
Question 3(c)
Research shows that there is a strong link between coffee consumption and anxiety in both adults and teenagers. Some findings suggest that there is a greater impact of coffee consumption on teenagers’ anxiety than on adults’. The table shows some of these findings.
A researcher claimed that teens are 80% more likely to be affected by anxiety due to coffee drinking than adults.
By first completing the table, evaluate this claim using calculations based on the data, and interpret the relative risks in context.
80
123
253
210
The relative risk of teenagers having coffee induced anxiety compared to adults having coffee induced anxiety is 1.797. This does support the claim that teenagers are approximately 80% MORE LIKELY to be affected by anxiety due to coffee drinking than adults.
However, keep in mind, this is only one study, and there may be other factors that this study did not look into that also may play a part in the results.