Larry is 2 years younger than Mary. The difference between the squares of their ages is 28. How old is each?

2 Answers
Jan 28, 2016

Answer:

Mary is #8#; Larry is #6#

Explanation:

Let
#color(white)("XXX")L # represent Larry's age, and
#color(white)("XXX")M # represent Mary's age.

We are told:
[equation 1]#color(white)("XXX")L=M-2#
and
[equation 2]#color(white)("XXX")M^2-L^2=28#

Substituting #M-2# from equation [1] for #L# in equation [2]
#color(white)("XXX")M^2-(M-2)^2=28#

#color(white)("XXX")M^2 - (M^2-4M+4)=28#

#color(white)("XXX")4M-4=28#

#color(white)("XXX")4M=32#

#color(white)("XXX")M=8#

Substituting #8# for #M# in equation [1]
#color(white)("XXX")L=8-2 = 6#

Jan 28, 2016

Answer:

#6 and 8#

Explanation:

Let the age of #Larry=x#

Age of #Mary=x+2# (Difference of their ages are 2)

Given that the difference between the squares of their ages is 28

So,#(2+x)^2-x^2=28#

Use the formula #(a+b)^2=a^2+2ab+b^2#

#rarr(4+4x+x^2)-x^2=28#

#rarr4+4x+x^2-x^2=28#

#rarr4+4x=28#

#rarr4x=28-4#

#4x=24#

#x=24/4=6#

We know now that the Age of

#Larry=6#

So, Age of #Mary=(x+2)=6+2=8#