Question

p grade 7 7.14 creating equations for proportional relationships to solve word problems (level 1)
the number of pages that anastasia reads is proportional to the number of minutes that she reads. it takes anastasia 120 minutes to read 90 pages in her book. write an equation in the form p = km that models the number of pages p that anastasia reads after reading for m minutes.
p =
how many pages does anastasia read in 100 minutes?

Explanation:

Step1: Find the rate of pages per minute

First, we need to find the constant of proportionality \( k \). The formula for a proportional relationship is \( p = kt \), where \( p \) is the number of pages, \( t \) is the time in minutes, and \( k \) is the constant rate. We know that when \( t = 120 \) minutes, \( p = 90 \) pages. So we can find \( k \) by \( k=\frac{p}{t}=\frac{90}{120}=\frac{3}{4} = 0.75\).

Step2: Write the equation

Now that we have \( k = 0.75 \), the equation in the form \( p=kt \) is \( p = 0.75t \) (or \( p=\frac{3}{4}t \)).

Step3: Calculate pages read in 100 minutes

To find how many pages Anastasia reads in 100 minutes, we substitute \( t = 100 \) into the equation \( p = 0.75t \). So \( p=0.75\times100 = 75 \).

Answer:

The equation is \( p = 0.75t \) (or \( p=\frac{3}{4}t \)) and the number of pages read in 100 minutes is 75.