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:

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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... 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

2/5 of these students do Business Studies.

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Answer

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

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

Thus, the number of students who do Business Studies is 34. To find the number of students who do not do Business Studies, subtract this from the total number of students:

$85 - 34 = 51$

So, the number of students who do not do Business Studies is 51.

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:

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

Substituting the values gives:

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

Rounding this to one decimal place, 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

The original ratio of students to teachers is 15:1.

After hiring one extra teacher, the new ratio remains as a:1, where a ∈ Q. Hence, the value of a must be less than 15, given that the total number of students hasn't changed. Thus, the correct statement is:

a < 15

An example to support this is:

Original ratio: 15 students for 1 teacher
New ratio after hiring one teacher (with the same number of students): 14 students per teacher (1 extra teacher added).

Hence, it demonstrates that a < 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

2/5 of these students 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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