Question

Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has written \dfrac{1}{4}
4



1



​ start fraction, 1, divided by, 4, end fraction as many articles as Mustafa has. Gia has written \dfrac{3}{2}



2



3



​ start fraction, 3, divided by, 2, end fraction as many articles as Mustafa has.



Write an inequality to determine the number of articles, mmm, Mustafa could have written for the school newspaper.



What is the solution set of the inequality?

Answer 1

Answer:

• m + m/4 + 3m/2 > 22
• m > 8 . . . . m restricted to multiples of 4, perhaps

Step-by-step explanation:

Let m represent the number of articles Mustafa has written. Then the total number of articles written must satisfy the inequality ...

  m +m/4 +3m/2 > 22

This has solution ...

  (11/4)m > 22

   m > (4/11)22

   m > 8 . . . . . . . . the solution to the inequality

If all the numbers are integers, and the ratios are exact, then we must have m be a multiple of 4 (that is, 4 times the number of articles Heloise wrote).

The solution set will be ...

  m ∈ {12, 16, 20, 24, ...} (multiples of 4 greater than 8)