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

Algebra Level 3

John ordered 4 4 pairs of black socks and some additional pairs of blue socks. The price of the black socks per pair was twice that of the blue. When the order was filled, it was found that the number of pairs of the two colors had been interchanged. This increased the bill by 50 50 %. The ratio of the number of the pairs of black socks to the number of pairs of blue socks in the original order can be expressed as a : b a:b in the simplified form. Find a + b a+b .


The answer is 5.

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5 solutions

Shamima Shimu
Mar 31, 2014

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.

Venture Hi
Mar 29, 2014

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

Frank Lo
Mar 31, 2014

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.

I didn't like anyone

Reazul Zannat - 7 years, 2 months ago

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