Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has writt

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Mustafa, Heloise, and Gia have written more than a combined total of 222222 articles for the school newspaper. Heloise has writt

en \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.

Mathematics

1 answer:

Svet_ta [12.7K] · Answer 1 · 2026-02-22T01:49:36+03:00

Answer:

The inequality used to calculate the number of articles written by Mustafa for his school paper is $x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$ .

Mustafa has authored over 8 articles.

Step-by-step explanation:

Details given:

Total combined number of articles = 22

Let 'x' represent the articles written by Mustafa.

Now stated:

Heloise has authored $\frac{1}{4}$ as many articles as Mustafa.

Heloise's articles number = $\frac{1}{4}x$

Gia has penned $\frac{3}{2}$ as many articles as Mustafa.

Gia's article count = $\frac{3}{2}x$

It follows that;

The total of articles from Mustafa, Heloise, and Gia must be more than or equal to the total combined articles.

Expressing it in an equation gives us;

$x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$

Thus the inequality for finding the number of articles penned by Mustafa for his school project is $x+\frac{1}{4}x+ \frac{3}{2}x\geq 22$ .

Now simplifying the inequality:

By taking the LCM to standardize the denominator, we get:

$\frac{x\times 4}{4}+\frac{1\times1}{4\times1}x+ \frac{3\times2}{2\times2}x\geq 22\\\\\frac{4x}{4}+ \frac{x}{4}+\frac{6x}{4}\geq 22\\\\\frac{4x+x+6x}{4} \geq 22\\\\11x\geq 22\times4\\\\11x\geq 88\\\\x\geq \frac{88}{11} \\\\x\geq 8$

Thus, Mustafa has written in excess of 8 articles.