Part (i)
Answer: 6x+12
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Explanation:
Jane's present age is x years old. We replace x with any positive whole number. Currently, Paul is 6 times as old as her, so Paul's current age is 6x years old. In 12 years time, his future age will be 6x+12 years old.
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Part (ii)
Answers:
- The equation is 6x+12 = 3(x+12)
- The equation solves to x = 8 which means Jane's present age is 8 years old.
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Explanation:
If Jane is x years old now, then she will be x+12 years old twelve years into the future. By this point, Paul is 3 times as old as she is, meaning
(Paul's future age) = 3*(Jane's future age)
6x+12 = 3*(x+12)
6x+12 = 3x+36
6x-3x = 36-12
3x = 24
x = 24/3
x = 8
Jane is currently 8 years old. This makes Paul to be 6x = 6*8 = 48 years old currently.
Twelve years from now, Jane and Paull will be 8+12 = 20 years old and 48+12 = 60 years old respectively. We can see that Paul will be three times older than she is since 20*3 = 60. This helps confirm we have the correct answers.
