Mrs Martini age is 42 years and Tony age is 12 years
Step-by-step explanation:
The given is:
- Mrs. Martini is 6 years more than 3 times as old as Tony
- Eight years ago, she was 2 years less than 9 times as old as he was then
Assume that Tony is x years old now
∵ Mrs. Martini is 6 years more than 3 times as old as Tony
∵ Tony is x years old
- Multiply the age of Tony by 3 and add 6 to the product
∴ The age of Mrs Martini = 3 x + 6
8 years ago
- Subtract 8 from the age of each one
Tony age = (x - 8)
Mrs Martini age = (3 x + 6) - 8 = 3 x + 6 - 8 = 3 x - 2
∵ Eight years ago, Mrs Martini was 2 years less than 9 times as old
as Tony was then
- Multiply Tony age by 9 and subtract 2 from the product
∵ Tony age from 8 years ago = x - 8
∵ Mrs Martini age from 8 years ago = 3 x - 2
∴ 9(x - 8) - 2 = 3 x - 2
- Simplify the left hand side
∴ 9 x - 72 - 2 = 3 x - 2
- Add like terms
∴ 9 x - 74 = 3 x - 2
- Subtract 3 x from both sides
∴ 6 x - 74 = -2
- Add 74 to both sides
∴ 6 x = 72
- Divide both sides by 6
∴ x = 12
∵ x represents the age of Tony
∴ Tony is 12 years old
∴ 3 x + 6 is the age of Mrs Martini
- Substitute x by 12
∵ 3(12) + 6 = 36 + 6 = 42
∴ Mrs Martini is 42 years old
Mrs Martini age is 42 years and Tony age is 12 years
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