CONFUSION... Which color did I buy???

If the price of each pair of Black socks = x & the number of pairs of blue socks = b,

Then, Correct price of Socks were = 4x + bx/2

And after interchange the price became = 4x/2 + bx

It made the price 1.5 times i.e. 3/2 times higher.

So,

4x/2 + bx = 3/2 (4x + bx/2)

2x + bx = 6x + 3bx/4

(4bx - 3bx)/4 = 6x - 2x

bx = 16x

b = 16.

Then the blue socks were 16 pairs.

So, the ratio = a : b = 4 : 16 = 1 : 4

And a + b = 5.

Price of black socks=$2x, price of blue socks=$x Initially he ordered 4 pairs of blacks and y pairs of blue. But the shipper switched his orders, so he got instead y pair of blacks and 4 pairs of blue. Set up the equality: Since the bill came up 50% more, therefore 3/22(2x 4)+x y)=(2x y+4 x) y=16 pairs

The ratio of blue:black=4:16 or 1:4

Let the number of blue socks be represented as b. We are informed that the price of the blue sock is twice the price of a black sock; let us assume that the price of one pair of black socks is $1. That means the price of one pair of blue socks is $2.

Now from the third and fourth sentence, we see that 1.5(1(4)+2(b))=1(b)+2(4). Simplifying gives b=1. This means the ratio of the number of pairs of black socks and the number of pairs of blue socks is \boxed{\textbf 4:1}

=4+1

=5

In this problem, assuming the price of the black socks as 100 per pair. The blue socks would be 50 per pair. Thus, the intended price is 4(100) + x(50), where x is the no. of blue pairs. If the order was wrong, and the colors were switched, the new price would be 4(50) + x(100), which is 150/100, or 3/2 into the original price.

(4(100) + x(50))*3/2=4(50) + x(100)

(200 + 25x)*3=200 + 100x

600 + 75x= 200 + 100x

25x = 400

x = 16

Thus, there were originally intended to be 16 pairs of socks The ratio of socks is therefore 16:4 or 4:1, which is a:b Thus, a + b = 5

a : 4 = 150 : 100 Hence, a = (150/100) x 4 = 6. the ratio of a : b is 6 : 4. When we simplify them, we get 3 : 2. so, 3+2 = 5.