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Question
Jen and Ariel are reading a 400 page novel for their literature class. Jen decides to read 100 pages the first day and 50 pages each day thereafter. Ariel's progress on reading the book is represented by the linear function y = 40x + 80, where y is the total number of pages read after x days thereafter. Which statement BEST compares Jen's reading rate each day to Ariel's daily reading rate?
Responses
A Jen reads 20 pages per day more than Ariel.Jen reads 20 pages per day more than Ariel.
B Ariel reads 10 pages per day less than Jen.Ariel reads 10 pages per day less than Jen.
C Ariel read 20 pages more the first day than Jen read.Ariel read 20 pages more the first day than Jen read.
D The reading rate each day for Jen and Ariel is the same.The reading rate each day for Jen and Ariel is the same.
To compare Jen's and Ariel's daily reading rates, we need to find the number of pages they read per day.
Jen reads 100 pages the first day and 50 pages each day thereafter. This can be represented by the formula: Jen's reading rate = 100 + 50x.
Ariel's progress on reading the book is represented by the linear function y = 40x + 80, where y is the total number of pages read after x days.
To compare their reading rates, we can equate the two formulas:
100 + 50x = 40x + 80.
Simplifying the equation, we get:
10x = -20.
Dividing both sides by 10, we get:
x = -2.
Since x represents the number of days, and we cannot have a negative number of days, we can conclude that the equations do not intersect, meaning that Jen's and Ariel's reading rates are not the same.
Therefore, the correct answer is B: Ariel reads 10 pages per day less than Jen.