It takes flora 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves. if she spent 65 hours knitting a total of 15 pairs of socks and gloves, how many pairs of each did she knit?

Flora can make 10 pairs of socks and 5 pairs of gloves.

Step-by-step explanation:

Here we have to form two equations from the given information.

Let "x" be the number of pair of socks and "y" be the number of pair of gloves.

Given:

It takes flora 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves. If she spent 65 hours knitting a total of 15 pairs of socks and gloves,

x + y = 15

3x + 7y = 65

Now we have to solve these two equations to find the solution.

Let's use the substitution method.

From the first equation can be written as

x = 15 - y

Now plug in x = 15 - y in the second equation and find the value of y.

3(15 - y) + 7y = 65 (This is called substitution method)

45 - 3y + 7y = 65

Simplify the like terms

45 + 4y = 65

Subtract 45 from both sides, we get

4y = 65 - 45

4y = 20

Dividing both sides by 4, we get

y = 20/4

y = 5

Now plug in y = 5 in the x = 15 - y

x = 15 - 5

x = 10

Therefore, Flora can make 10 pairs of socks and 5 pairs of gloves.