Question

It takes Flora 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves. If she spent 100 hours knitting a total of 16 pairs of socks and gloves, how many pairs of each did she knit?

Answer 1

3 pairs of socks and 13 pairs of gloves

Answer 2

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.