There are 85 students in third year in Liam's school. (a) 2/5 of these students do Business Studies. Work out the number of these students who do not do Business Studies. (b) 26 of the students in third year do Art. Work out the percentage of students in third year who do Art, correct to one decimal place. The ratio of students to teachers in Liam's school was 15:1. The school hired one extra teacher, while the number of students stayed the same. The new ratio of students to teachers was a:1, where a ∈ Q. (c) Put a tick (✓) in the correct box to show which statement is true. Tick one box only. Give an example to support your answer. a > 15 a = 15 a < 15 Example:

Junior Cycle Mathematics Counting/Permutations: There are 85 students in third y

There are 85 students in third year in Liam's school - Junior Cycle Mathematics - Question 1 - 2019

Question 1

There are 85 students in third year in Liam's school. (a) 2/5 of these students do Business Studies. Work out the number of these students who do not do Business S... show full transcript

Worked Solution & Example Answer:There are 85 students in third year in Liam's school - Junior Cycle Mathematics - Question 1 - 2019

Step 1

Work out the number of these students who do not do Business Studies.

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Answer

To find the number of students who do Business Studies, calculate:

$n = \frac{2}{5} \times 85 = 34$

Now subtract this from the total number of students:

$85 - 34 = 51$

Thus, 51 students do not do Business Studies.

Step 2

Work out the percentage of students in third year who do Art, correct to one decimal place.

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Answer

To find the percentage of students who do Art, use the formula:

$\text{Percentage} = \left( \frac{\text{Number of students doing Art}}{\text{Total number of students}} \right) \times 100$

Plugging in the values:

$\text{Percentage} = \left( \frac{26}{85} \right) \times 100 = 30.588... \approx 30.6\%$

Thus, the percentage of students who do Art is 30.6%.

Step 3

Put a tick (✓) in the correct box to show which statement is true.

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Answer

To find the new ratio after hiring one extra teacher:

The original ratio is 15:1, meaning there are 15 students for every 1 teacher.

With one extra teacher, the new teacher count becomes: 1 + 1 = 2. Therefore, if the number of teachers is now 2, the number of students is:

$15 \times 1 = 15$

So, we have 15 students and 2 teachers, leading to a new ratio of:

$\frac{15}{2} = 7.5:1$

Thus, a < 15 is true. An example would be:

If a = 7.5, then 7.5 < 15.

There are 85 students in third year in Liam's school - Junior Cycle Mathematics - Question 1 - 2019

Worked Solution & Example Answer:There are 85 students in third year in Liam's school - Junior Cycle Mathematics - Question 1 - 2019

Work out the number of these students who do not do Business Studies.

Work out the percentage of students in third year who do Art, correct to one decimal place.

Put a tick (✓) in the correct box to show which statement is true.

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