Question

John reads 5 books every 3 months. Create an algebraic equation to represent y, the total number of books read in x months.

A. y = 5x
B. y = 5x/3
C. y = 3x/5
D. y = x/5

Answer 1

B. y = 5x/3

Step-by-step explanation:

"John reads 5 books every 3 months." can be made into a conversion factor:

(5 books)/(3 months) is (5/3) books/month. If x is time, in months, then (5/3)x would be the total number of books read in x months, assuming John has no other life and maintains his (5/3) books/month rate.

If y is the total number of books, then y = (5/3)x is the total number of books read in x months.

y = (5/3)x or y = 5x/3

B. y = 5x/3

Answer 2

The correct algebraic equation that represents y, the total number of books read in x months, is y = (5/3)x, which is a linear equation demonstrating a direct relationship between months and books read.

Step-by-step explanation:

The student has asked to create an algebraic equation to represent y, the total number of books read in x months, given that John reads 5 books every 3 months. To create the equation, we have to figure out how many books he would read in just one month, which would be 5 books divided by 3 months. This gives us the rate of books per month. Therefore, the algebraic equation that represents the relationship is y = (5/3)x. This means for every month (x), we multiply it by 5/3 to get the total number of books (y).

The main explanation for the equation is that it's a direct relationship between the number of months and the number of books read, which can be classified as a linear equation, similar to the examples provided such as y = 6x + 8 and y = 9 + 3x, where you have a constant rate of change (the number of books per month in this case).