Lenny is eight years older than twice her cousin Sue's age. The sum of their ages is less than 32. What is the greatest age that Sue could be?

1 Answer
Jul 8, 2018

Sue can be, at greatest, 7 years of age.

Explanation:

Lenny's age is #L#.
Lenny is eight years older(8+) than twice her cousin Sue's age (2S, as #S# is Sue's age)

Therefore,
#\color(red)(L=8+2S)#

The sum of their (Lenny and Sue) ages is less than 32.
#L+S\lt32#

Do you notice that there is already an equation for #L# that contains #S# (in red)? Let's substitute that into the inequality we just mentioned.

#(\color(red)(8+2S))+S\lt32#
Simplifying...
#8+3S\lt32#
#3S\lt32-8#
#3S\lt24#
#S\lt24/3#
#S\lt8#

Since Sue cannot be 8, the oldest (greatest age) she can be is 7 years old.