Dante is fourteen years older than Maggie. Eight years ago, Dante was three times as old as Maggie. Find their ages three years from now.

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UK2019IN UK2019IN · Answer 1

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[tex]\underline{\mathbb{PROBLEM:}}[/tex]

Dante is fourteen years older than Maggie. Eight years ago, Dante was three times as old as Maggie. Find their ages three years from now.

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[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex]\qquad\Large\rm» \:\: \green{Dante\:is\:26\:years\:old}[/tex]

[tex]\qquad\Large\rm» \:\: \green{Maggie\:is\:12\:years\:old}[/tex]

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[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- Represent x and y as the ages of Dante and Maggie respectively. Formulated equations of the given statement

[tex] \begin{cases}x = 14 + y& \red{(eq. \: 1)} \\x - 8 = 3(y - 8)& \red{(eq. \: 2)} \end{cases}[/tex]

- Substitute x from the first equation to the second equation in terms of y which is the age of Maggie before 3 years.

[tex] \begin{cases}x = 14 + y \\ \text - 3y + y = \text - 24 + 6 \end{cases}[/tex]

[tex] \begin{cases}x = 14 + y \\ \begin{gathered} \frac{ \cancel{\text -2}y}{ \cancel {\text - 2}} = \frac{\text -18}{ \text - 2} \end{gathered} \end{cases}[/tex]

- The age of Maggie before 3 years is 9 years old, then substitute it to the first equation to find Dante's age.

- The age of Dante before 3 years is 23 years old. Find their ages after 3 years of their present ages.

Present Age of Dante:

Present Age of Maggie:

[tex]\therefore[/tex] Dante is 26 years old while Maggie is 12 years old.

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