Martin creates a pattern of numbers using the instructions in the table below - Junior Cycle Mathematics - Question 12 - 2015
Question 12
Martin creates a pattern of numbers using the instructions in the table below.
The first number is filled in.
(a) Complete the table.
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Worked Solution & Example Answer:Martin creates a pattern of numbers using the instructions in the table below - Junior Cycle Mathematics - Question 12 - 2015
Step 1
Complete the table.
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Answer
To complete the table, we will follow the instructions for each number.
Starting Number:
First Number: 5
Second Number: 6
Third Number: 7
Multiply by 3:
First Number: 5×3=15
Second Number: 6×3=18
Third Number: 7×3=21
Subtract 5 from your answer:
First Number: 15−5=10
Second Number: 18−5=13
Third Number: 21−5=16
Thus, the completed table is:
Instruction
First Number
Second Number
Third Number
Starting Number
5
6
7
Multiply by 3
15
18
21
Subtract 5 from your answer
10
13
16
Step 2
Martin picks a starting number and, using the instructions, gets an outcome of 1. Find the starting number he picked.
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Answer
Let the starting number be x. According to the instructions, we have:
Multiply by 3: 3x
Subtract 5: 3x−5=1
To solve for x, we rearrange the equation:
3x−5=13x=1+53x=6x=2
Thus, the starting number picked by Martin is 2.
Step 3
When the starting number is k, what is the outcome? Give your answer in terms of k.
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Answer
Let the starting number be k. Using the same operations as before:
Multiply by 3:
Outcome after multiplication: 3k
Subtract 5:
Final outcome: 3k−5
Thus, when the starting number is k, the outcome is 3k−5.
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