Final answer:
To express y in terms of v, we equate the two equations derived from the division of x by 5 and by 4, respectively. Upon solving for y, we find that y = 4v + 1, making (b) the correct choice.
Step-by-step explanation:
When a whole number x is divided by 5 the quotient is y, and the remainder is 4, which can be written as x = 5y + 4. Similarly, when x is divided by 4 the quotient is v, and the remainder is 1, which can be expressed as x = 4v + 1. To express y in terms of v, we need to make x the subject in both equations and then set them equal to each other since they both represent the original number x.
By equating the equations: 5y + 4 = 4v + 1, we need to solve for y. So, subtract 4 from both sides to isolate the terms with y: 5y = 4v - 3. Then, divide both sides by 5 to solve for y: y = (4v - 3)/5. However, since v is a whole number and we are told that the remainder when x is divided by 5 is 4, the quotient must be one less than it would be if the remainder were 0.
Therefore, we add 1 to the result: y = 4v/5 - 3/5 + 1, which simplifies to y = (4v - 3 + 5)/5, and further simplification gives us y = 4v/5 + 2/5. We know that y must also be an integer (because it is a division quotient), and the only way for that to happen is if the remainder from the division by 5 is indeed 4, meaning that we must add another whole number to our equation. This leads us to y = 4v + 1, as option (b) suggests.