Question

1. higher order thinking in 4th grade, richard read 37 books. in 5th grade, he read 9 more books than the year before. this year, in 6th grade, richard plans to read at least 12 more books than the total number of books read in both 4th and 5th grades. richard writes the inequality ( b geq 130 ) to show the total number of books he will have read in 4th, 5th, and 6th grades. is his inequality correct? why or why not?

Explanation:

Step1: Find books read in 5th grade

Richard read 37 books in 4th grade. In 5th grade, he read 9 more books than 4th grade. So, number of books in 5th grade = \( 37 + 9 = 46 \)

Step2: Find total books read in 4th and 5th grade

Total books in 4th and 5th grade = \( 37 + 46 = 83 \)

Step3: Find minimum books read in 6th grade

In 6th grade, he plans to read at least 12 more books than total of 4th and 5th grade. So, minimum books in 6th grade = \( 83 + 12 = 95 \)

Step4: Find total books read in 4th, 5th, and 6th grade

Total books \( b = 37 + 46 + 95 = 178 \) (minimum total). Wait, but Richard wrote \( b \geq 180 \). Let's re - calculate total properly. Total books read in 4th and 5th is \( 37+(37 + 9)=37 + 46 = 83 \). Let the number of books in 6th grade be \( x \), where \( x\geq83 + 12=95 \). Then total books \( b=37 + 46+x=83 + x \). Since \( x\geq95 \), then \( b = 83+x\geq83 + 95=178 \). So the correct inequality should be \( b\geq178 \), not \( b\geq180 \). So his inequality is not correct.

Answer:

Richard's inequality \( b\geq180 \) is not correct. The correct minimum total number of books he will have read is \( 37+(37 + 9)+(37 + 9+12)=37 + 46+95 = 178 \), so the inequality should be \( b\geq178 \), not \( b\geq180 \).