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.

Answer 1

inequality - m+ 1/4m + 3/2m > 22

solution set - m>8

Explanation:

Answer 2

The Inequality For determining number of equation written by Mustafa for school paper is
`x+(1)/(4)x+ (3)/(2)x\geq 22`.

Mustafa has written more than 8 articles.

Explanation:

Given:

Combined Total Number of articles = 22

Let the number of articles written by Mustafa be 'x'.

Now Given:

Heloise has written
`(1)/(4)` as many articles as Mustafa has.

Number of article written by Heloise =
`(1)/(4)x`

Gia has written
`(3)/(2)` as many articles as Mustafa has.

Number of article written by Gia =
`(3)/(2)x`

Now we know that;

The sum of number of articles written by Mustafa and Number of article written by Heloise and Number of article written by Gia is greater than or equal to Combined Total Number of articles.

framing in equation form we get;

`x+(1)/(4)x+ (3)/(2)x\geq 22`

Hence the Inequality For determining number of equation written by Mustafa for school paper is
`x+(1)/(4)x+ (3)/(2)x\geq 22`.

Now Solving the Inequality we get;

Taking LCM for making the denominator common we get:

`(x* 4)/(4)+(1*1)/(4*1)x+ (3*2)/(2*2)x\geq 22\\\\(4x)/(4)+ (x)/(4)+(6x)/(4)\geq 22\\\\(4x+x+6x)/(4) \geq 22\\\\11x\geq 22*4\\\\11x\geq 88\\\\x\geq (88)/(11) \\\\x\geq 8`

Hence Mustafa has written more than 8 articles.