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Eoin is E years old - Junior Cycle Mathematics - Question 11 - 2018

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Eoin is E years old. Complete the table below by writing the age of each of the other people in terms of E. | Person | Description of their age | Age, ... show full transcript

Worked Solution & Example Answer:Eoin is E years old - Junior Cycle Mathematics - Question 11 - 2018

Step 1

Complete the table below by writing the age of each of the other people in terms of E.

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Answer

  1. Grace: Eoin is E years old, so Grace, being 7 years younger than Eoin, is E - 7 years old.

  2. Evan: Since Evan is twice as old as Eoin, he is 2E years old.

  3. Aoibhe: Aoibhe is 3 years older than Eoin, making her E + 3 years old.

Step 2

Grace is half Eoin’s age.

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Answer

Let Eoin's age be represented as E. Since Grace is half of Eoin's age, we can write the equation:

G=12EG = \frac{1}{2}E

From the previous part, we know that Grace's age is also given by:
G=E−7G = E - 7

Setting these equations equal to each other:
12E=E−7\frac{1}{2} E = E - 7

To solve for E, we first eliminate the fraction by multiplying every term by 2:
E=2(E−7)E = 2(E - 7)
E=2E−14E = 2E - 14

Rearranging gives:
E−2E=−14E - 2E = -14
−E=−14-E = -14
E=14E = 14

Thus, Eoin’s age is 14 years.

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