Answer: at most 15 pairs of socks
Step-by-step explanation:
Let the number of pair of socks of her sister be
, and let the number of pairs Lucy has be
.
Since , Lucy has 4 more than 1/3 the number of pairs of socks as her sister, this means that
.............................. equation 1
Also , Lucy has at most 9 pairs of socks , this means that
....................................... equation 2
Equating the two equations , we have
![\frac{1}{3}x + 4 \leq 9](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7Dx%20%2B%204%20%5Cleq%209)
multiply through by 3
![x + 12\leq 27](https://tex.z-dn.net/?f=x%20%2B%2012%5Cleq%2027)
subtract 12 from both sides
![x\leq 15](https://tex.z-dn.net/?f=x%5Cleq%2015)
Therefore , the sister has at most 15 pairs of socks