Michael is 6 times as old as his granddaughter Lauraa. If Laura’s present age is x years, write down in terms of x the age of Michael in 15 years time.b. In 15 years time, Michael will be 3 times as old as Laura. Write an equation in x and hence findtheir present ages.
Question
Michael is 6 times as old as his granddaughter Lauraa. If Laura’s present age is x years, write down in terms of x the age of Michael in 15 years time.b. In 15 years time, Michael will be 3 times as old as Laura. Write an equation in x and hence findtheir present ages.
Solution
a. If Laura's present age is x years, then Michael's present age is 6x years. In 15 years time, Laura will be x + 15 years old and Michael will be 6x + 15 years old.
b. According to the problem, in 15 years time, Michael will be 3 times as old as Laura. So, we can write the equation as follows:
6x + 15 = 3(x + 15)
Solving this equation will give us their present ages.
First, distribute the 3 on the right side of the equation:
6x + 15 = 3x + 45
Then, subtract 3x from both sides to get:
3x + 15 = 45
Next, subtract 15 from both sides to get:
3x = 30
Finally, divide both sides by 3 to solve for x:
x = 10
So, Laura is 10 years old and Michael is 6 * 10 = 60 years old.
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