SOLUTION: Freddy is 3 years older than 6 times his grandson's age. The sum of their ages is greater than 67. What is the youngest age Freddy's grandson can be?
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Question 1198772: Freddy is 3 years older than 6 times his grandson's age. The sum of their ages is greater than 67. What is the youngest age Freddy's grandson can be? Found 2 solutions by Theo, ikleyn:Answer by Theo(13342) (Show Source):
replace x with 6y + 3 in the inequality to get:
6y + 3 + y > 67
combine like terms to get:
7y + 3 > 67
subtract 3 from both sides of the inequality to get:
7y > 64
solve for y to get:
y > 64/7
that should be your solution.
you have to solve the equation and the inequality simultaneously.
the common solution is when y > 64/7.
when y > 64/7, x = 6y + 3 will be greater than 405/7 and x + y will be greater than 67.
the solution appears to be that y > 64/7.
the youngest freddy's grandson can be is some amount of age greater than 64/7 years.
it can not be 64/7 because then x = 6y + 3 would become x = 405/7 and 405/7 + 64/7 would be equal to 67 which is not allowed because x + y must be greater than 67.
y > 64/7 appears to be your solution.
that means that the grandson's age has to be greater than 64/7
it can also be shown as y > 9 + 1/7
it can also be shown as y > 9.142857143, depending on how many digits your calculator can display.
Let x be the Freddy grandson's age.
Then Freddy's age is (6x+3) years.
The problem says that
x + (6x+3) > 67.
It implies
7x > 67 - 3
7x > 64
x > 64/7 = 9.
Since the age is an integer number of years, from the last inequality we can conclude that x >= 10.
In other words, Freddy's grandson is at lest 10 years old.
10 years is the youngest age of the Freddy's grandson.
