Answer: Flora knitted 3 pairs of socks and 13 pairs of gloves.
Step-by-step explanation: Given that Flora takes 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves and she spent 100 hours knitting a total of 16 pairs of socks and gloves.
We are to find the number of pairs of socks and gloves that she knitted.
Let a and b denote the number of pairs of socks and gloves respectively that she knitted.
Then, according to the given information, we have
\(a+b=16~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3a+7b=100~~~~~~~~~~~~~~~~~~~(ii)\)
Multiplying equation (i) by 3, we have
\(3(a+b)=3\times 16\\\\\Rightarrow 3a+3b=48~~~~~~~~~~~~~~~~~~~~~(iii)\)
Subtracting equation (iii) from equation equation (ii), we get
\((3a+7b)-(3a+3b)=100-48\\\\\Rightarrow 7b-3b=52\\\\\Rightarrow 4b=52\\\\\Rightarrow b=\dfrac{52}{4}\\\\\Rightarrow b=13.\)
From equation (i), we get
\(a+b=16\\\\\Rightarrow a=16-13\\\\\Rightarrow a=3.\)
Thus, Flora knitted 3 pairs of socks and 13 pairs of gloves.