Chapter 2: Introduction to Linear Polynomials

Exercise

Question

Question: 3

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The present age of Salil's mother is three times Salil's present age. After 5 years, their ages will add up to 70 years. Find their present ages.

Answer

1
Let Salil's present age be x years. Express his mother's present age using the given relationship.
Salil's present age = $x$ years
\text{Mother's present age = $3x$ years $\quad$ ${color:#625b5f}[Salil's mother is 3 times Salil's present age.]{/color}$}
2
Find their ages after 5 years.
Salil's age after 5 years = $(x + 5)$ years
Mother's age after 5 years = $(3x + 5)$ years
3
Use the sum of their ages after 5 years to form an equation and solve it for x.
\text{$(x + 5) + (3x + 5) = 70$ $\quad$ ${color:#625b5f}[The sum of their ages will be 70 years after 5 years.]{/color}$}
⇒
$4x + 10 = 70$
⇒
$4x = 70 - 10$
⇒
$4x = 60$
⇒
\text{ $x = \dfrac{60}{4} = 15$ years $\quad$ ${color:#625b5f}[Salil's present age]{/color}$}
4
Substitute x = 15 to find his mother's present age.
\text{Mother's present age = $3x = 3 × {color:#2E2EFF}15{/color} = 45$ years}
5
Write the present ages of Salil and his mother.
Answer: Salil is 15 years old and his mother is 45 years old.
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