Jiya’s mother is 12 years more than twice her age. After 8 years, her mother’s agewill be 20 years less than three times her age. Find Jiya’s age and her mother’s age
Question
Jiya’s mother is 12 years more than twice her age. After 8 years, her mother’s agewill be 20 years less than three times her age. Find Jiya’s age and her mother’s age
Solution
Let's solve the problem step by step:
Step 1: Let's assume Jiya's age as x.
Step 2: According to the problem, Jiya's mother is 12 years more than twice Jiya's age. So, Jiya's mother's age can be represented as 2x + 12.
Step 3: After 8 years, Jiya's age will be x + 8, and her mother's age will be 2x + 12 + 8 = 2x + 20.
Step 4: According to the problem, her mother's age after 8 years will be 20 years less than three times Jiya's age. So, we can write the equation as 2x + 20 = 3(x + 8) - 20.
Step 5: Simplifying the equation, we get 2x + 20 = 3x + 24 - 20.
Step 6: Combining like terms, we get 2x + 20 = 3x + 4.
Step 7: Subtracting 2x from both sides, we get 20 = x + 4.
Step 8: Subtracting 4 from both sides, we get 16 = x.
Step 9: Therefore, Jiya's age is 16 years.
Step 10: Substituting the value of x in the equation for Jiya's mother's age, we get Jiya's mother's age as 2(16) + 12 = 44 years.
So, Jiya is 16 years old and her mother is 44 years old.
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