Question

Angelo has a drawer full of black and white socks. There are a total of 31 socks in the drawer. Half the number of black plus one-third the number of white is fourteen. How many of each colour does he have?

Answer 1

Let

x ----> number of black socks

y ----> number of white socks

we have that

x+y=31 ------> x=31-y -----> equation 1

(1/2)x+(1/3)y=14 -----> equation 2

Solve the system of equations

substitute equation 1 in equation 2

(1/2)(31-y)+(1/3)y=14

solve for y

(31/2)-(1/2)y+(1/3)y=14

(1/2)y-(1/3)y=(31/2)-14

(1/6)y=3/2

y=18/2

y=9

Find out the value of x

x=31-y --------> x=31-9

x=22

therefore

number of black socks: 22

number of white socks: 9