Amy is eight years older than twice her cousin Alicia’s age. The sum of their ages is less than 32. Let x represent Alicia's age. Which inequality represents Alicia’s possible age?

a) 0<x≤24

b) 0<x<8

c) 0<x≤8

d) 0<x<24

2 Answers
Alan P.
Sep 7, 2017

b) # 0 < x < 8#

Explanation:

#{: (ul("Alicia"),color(white)("xxx"),ul("Amy")), (x,,2x+8) :}#

We are told
#color(white)("XXX")xcolor(white)("xx")+color(white)("xx)2x+8 <32#

#rarrcolor(white)("XXX")3x+8 <32#

#rarrcolor(white)("XXX")3x < 24#

#rarrcolor(white)("XXX")x < 8#

Technically I think the answer should have been #0 color(red)(<=) x < 8#
but that wasn't one of the available choices.

Truong-Son N.
Sep 7, 2017

Let Alicia's age be represented by #x#, and Amy's age be represented by #y#. Then since Amy is eight years older than twice Alicia's age, we say that

#y = 2 cdot overbrace(x)^"Alicia's age" + 8#

represents Amy's age. We also know that their combined ages are less than #32#:

#x + 2x + 8 < 32#

#=> 3x + 8 < 32#

#=> 3x < 24#

#=> ul(x < 8)#

So Alicia must be younger than #8#. Alicia also cannot be exactly #0# years old, because then she wouldn't be born yet (#0# years old implies #0# seconds old and so on). So, I would say Alicia's age is:

#color(blue)(0 < x < 8)#

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