Question

exercise 5
shontelle solves three math problems in four minutes.
a. use this information to complete the table below.

number of questions	number of minutes
6
9
12
15
18
21
24
27
30

b. shontelle has soccer practice on thursday evening. she has a half - hour before practice to work on her math homework and to talk to her friends. she has 20 math skill work questions for homework, and she wants to complete them before talking with her friends. how many minutes will shontelle have left after completing her math homework to talk to her friends?
use a double number line diagram to support your answer, and show all work.

Explanation:

Step1: Find the rate of solving questions

Shontelle solves 3 math problems in 4 minutes. The rate is $\frac{3}{4}$ questions per minute.

Step2: Complete the table

For 6 minutes: Number of questions = $\frac{3}{4}\times6=\frac{18}{4} = 4.5$
For 9 minutes: Number of questions = $\frac{3}{4}\times9=\frac{27}{4}=6.75$
For 12 minutes: Number of questions = $\frac{3}{4}\times12 = 9$
For 15 minutes: Number of questions = $\frac{3}{4}\times15=\frac{45}{4}=11.25$
For 18 minutes: Number of questions = $\frac{3}{4}\times18=\frac{54}{4}=13.5$
For 21 minutes: Number of questions = $\frac{3}{4}\times21=\frac{63}{4}=15.75$
For 24 minutes: Number of questions = $\frac{3}{4}\times24 = 18$
For 27 minutes: Number of questions = $\frac{3}{4}\times27=\frac{81}{4}=20.25$
For 30 minutes: Number of questions = $\frac{3}{4}\times30=\frac{90}{4}=22.5$

She has 30 minutes before practice. She has 20 math - skill work questions.
Time taken to complete 20 questions = $20\div\frac{3}{4}=20\times\frac{4}{3}=\frac{80}{3}\approx26.67$ minutes.
Time left = $30-\frac{80}{3}=\frac{90 - 80}{3}=\frac{10}{3}\approx3.33$ minutes.

Answer:

Number of Minutes	Number of Questions
6	4.5
9	6.75
12	9
15	11.25
18	13.5
21	15.75
24	18
27	20.25
30	22.5

She will have about 3.33 minutes left after completing her 20 math - skill work questions.