Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper. Heloise has written 1/4 as many articles as Mustafa has. Gia has written 3/2 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?
Inequality: m+1/4m+3/2m>22
Solution: m>8
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Well, well, well, let's see what we have here! So we have Mustafa, Heloise, and Gia who have written more than a total of 22 articles.
Now, we know that Heloise has written 1/4 as many articles as Mustafa and Gia has written 3/2 as many articles as Mustafa.
So let's crunch some numbers and put this into an inequality! Let's say Mustafa wrote m articles.
Heloise has written 1/4 m articles and Gia has written 3/2 m articles.
Therefore, the inequality would be:
m + (1/4)m + (3/2)m > 22
To solve this inequality and find the solution set, we need to simplify it.
Combining like terms, we have:
(7/4)m > 22
To get rid of that pesky fraction, let's multiply both sides of the inequality by 4/7:
(4/7)(7/4)m > (4/7)(22)
m > 8
So, my friend, the solution set for the inequality is m > 8. That means Mustafa must have written more than 8 articles for the school newspaper.
I hope that puts a smile on your face!
To solve this problem, let's start by assigning variables to the number of articles written by each person. Let m represent the number of articles written by Mustafa, h represent the number of articles written by Heloise, and g represent the number of articles written by Gia.
From the given information, we can write the following equations:
h = 1/4m (Heloise has written 1/4 as many articles as Mustafa)
g = 3/2m (Gia has written 3/2 as many articles as Mustafa)
We are also given that the combined total of their articles is greater than 22:
m + h + g > 22
Now let's substitute the values of h and g from the equations above into the inequality:
m + 1/4m + 3/2m > 22
To simplify the inequality, let's find a common denominator:
Multiply 1/4 by 2/2 to get 2/8, and multiply 3/2 by 4/4 to get 12/8.
m + 2/8m + 12/8m > 22
Combine like terms:
m + 14/8m > 22
Add the fractions:
22/1m + 14/8m > 22
Now let's find a common denominator for the fractions:
The common denominator is 8, so multiply the first fraction by 8/8 to get 22/8m, and the second fraction by 1/1 to keep it the same.
22/8m + 14/8m > 22
Combine like terms:
36/8m > 22
Simplify:
9/2m > 22
To further simplify, we can multiply both sides of the inequality by 2/9:
m > (22 * 2) / 9
m > 44/9
Therefore, the solution set of the inequality is m > 44/9.
whats the ineqaulity
m + h + g >/= 22
h = m/4
g = (3/2) m
now
m + m/4 + 3 m/2 >/= 22
multiply both sides by 4
4 m + m + 6 >/= 88
11 m >/= 88
divide both sides by 11 :)