John ordered 4 pairs of black socks and some additional pair 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%. The ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was:__________(A) 4:1(B) 2:1(C) 1:4(D) 1:2(E) 1:8

Step-by-step explanation: Given that John ordered 4 pairs of black socks and some additional pair 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%.

We are to find the ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order.

Let b represents the number of pairs of blue socks that John ordered and p be the price per pair of blue socks.

Then, the price of the black socks per pair = 2p.

The total price of the socks originally is

[tex]C=4\times2p+b\times p=8p+bp[/tex]

and the cost of the socks after interchange of the colors is

[tex]C'=4\times p+b\times2p=4p+2bp.[/tex]

According to the given information, we have

[tex](4p+2bp)-(8p+bp)=50\%\times(8p+bp)\\\\\Rightarrow 4p+2bp=\dfrac{8p+bp}{2}+(8p+bp)\\\\\Rightarrow 4p+2bp=\dfrac{3}{2}(8p+bp)\\\\\Rightarrow 4+2b=\dfrac{3}{2}(8+b)\\\\\Rightarrow 8+4b=24+3b\\\\\Rightarrow b=16.[/tex]

So, there are 16 pairs of blue socks.

Therefore, the ratio of the number of pairs of black socks to the number of pairs of blue socks in the original order was

[tex]4:16=\drac{4}{16}=\drac{1}{4}=1:4.[/tex]

Thus, option (C) is CORRECT.