Question

Max has a drawer full of green and red socks. He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks. Half the number of green socks plus one-third of the number of red socks is 36. How many of each colour does he have?

Answer 1

There are 42 red colour socks and 44 green color socks

Explanation:

Let there are r red socks and g green socks.

ATQ,

He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks.

4g-3r=50 ....(1)

Half the number of green socks plus one-third of the number of red socks is 36.

`(g)/(2)+(r)/(3)=36\\\\3g+2r=216\ .....(2)`

Multiply equation (1) by 2 and equation (2) by 3.

8g-6r = 100 ....(3)

9g +6r = 648 ....(4)

Add equation (3) and (4)

8g-6r + 9g +6r = 100+648

17g = 748

g = 44

Put the value of g in equation (1).

4(44)-3r=50

176-3r = 50

176-50 = 3r

r = 42

Hence, there are 42 red colour socks and 44 green color socks.