it girl it twice as old as her sister four years hence, the
product of their ages (in years) will be 160 find this present a
age
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Solution:
Let the present age of her sister be x years.
Then, the girl's present age = 2x years.
Product of their ages 4 years hence = (x + 4)(2x + 4).
∴ (x + 4)(2x + 4) = 160
[tex][/tex]
→ 2x² + 12x -144 = 0
→ x² + 6x - 72 = 0
→ x² + 12x - 6x - 72 = 0
→ x(x + 12) - 6(x + 12) = 0
→ (x + 12)(x - 6) = 0
→ x + 12 = 0 or x - 6 = 0
→ x = -12 or x = 6
→ x = 6 (the present age cannot be negetive)
∴ Sister's present age = 6 years and girl's present age = 12 years.
________________________
Answer :
Present ages of:
- Girl = 12 years.
- Her sister = 6 years.
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