Gabriella has between 2 and 3 hours to spend on Math, Sociology, and English homework. She plans to spend equal amounts of time studying Sociology and English, and to spend 2 times as much time studying Math as in studying Sociology.
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To find out how much time Gabriella will spend on each subject, we'll use algebraic equations. Let's assign variables to the time spent on each subject.
Let's say Gabriella spends x hours on Sociology.
Since she spends equal amounts of time on Sociology and English, she will also spend x hours on English.
According to the given condition, Gabriella will spend 2 times as much time on Math as on Sociology. So she spends 2x hours on Math.
The total time Gabriella spends on all three subjects can be represented by the equation:
x + x + 2x = 2-3 hours
Adding the time spent on each subject, we get:
4x = 2-3 hours
To solve for x, we can divide both sides of the equation by 4:
4x/4 = (2-3 hours)/4
x = 1/2 - 3/4 hours
Since Gabriella cannot spend negative time on her homework, we can ignore the negative solution. Therefore, the only valid value for x is 1/2 - 3/4 hours.
So, Gabriella will spend 1/2 - 3/4 hours on Sociology, which is equal to 1/4 hour or 15 minutes. Since she spends equal time on English, she will also spend 15 minutes on English. Finally, since she spends 2 times as much time on Math as Sociology, she will spend 2 * 15 minutes = 30 minutes on Math.
So, Gabriella will spend 15 minutes on Sociology, 15 minutes on English, and 30 minutes on Math.