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): You can put this solution on YOUR website!
let x = freddy's age.
let y = his grandson's age.

you have an equation and an inequality.

the equation is x = 6y + 3

the inequality is x + y > 67

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.

that's what i get.

Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

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.

Solved.



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