Answer: at most 15 pairs of socks
Step-by-step explanation:
Let the number of pair of socks of her sister be [tex]x[/tex] , and let the number of pairs Lucy has be [tex]y[/tex].
Since , Lucy has 4 more than 1/3 the number of pairs of socks as her sister, this means that
[tex]\frac{1}{3}x + 4 = y[/tex] .............................. equation 1
Also , Lucy has at most 9 pairs of socks , this means that
[tex]y\leq 9[/tex] ....................................... equation 2
Equating the two equations , we have
[tex]\frac{1}{3}x + 4 \leq 9[/tex]
multiply through by 3
[tex]x + 12\leq 27[/tex]
subtract 12 from both sides
[tex]x\leq 15[/tex]
Therefore , the sister has at most 15 pairs of socks
