Question

It takes flora 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves. if she spent 89 hours knitting a total of 15 pairs of socks and gloves, how many pairs of each did she knit?

Answer 1

s- number of pair of socks
g-number of pair of gloves

3*s+7*g=89
s+g=15 ⇒ s= 15-g

3*(15-g)+7g=89
3*15-3g+7g=89
45+4g=89
4g=89-45
4g=44
g=44/4
g=11
s=15-11
s=4

Answer 2

She knit 4 pairs of socks and 11 pairs of gloves.

Explanation:

Let x be the number of pair of socks and y be the number pair of gloves she knit,

Since, she knit 15 pairs of socks and gloves,

⇒ x + y = 15 ------(1)

Also, she spent 89 hours in knitting in which she took 3 hours to knit a pair of socks and 7 hours to knit a pair of gloves,

⇒ 3x + 7y = 89 -----(2),

Equation (2) - 3 × Equation (1),

We get,

7y - 3y = 89 - 45

⇒ 4y = 44

Dividing both sides by 4,

⇒ y = 11,

From Equation (1),

x + 11 = 15

⇒ x = 15 - 11 = 4,

Hence, She knit 4 pairs of socks and 11 pairs of gloves.