Question
In a classroom, the combined average age of all students
and their teacher is 17 years. The average age of the boys in the class is 13 years. If the teacher's age is 23 years more than the average age of the girls, and the number of boys is equal to the number of girls, what is the average age of the girls?Solution
Let number of boys in the class be x Then, number of girls in the class = x Total age of boys = 13x Let the average age of girls be a years Total age of girls = ax Age of teacher = a + 23 Total age of the class = 13x + ax + a + 23 Total number of people in the class = x + x + 1 = 2x +1 Average age of the class = (13x + ax + a + 23)/ (2x + 1) (13x + ax + a + 23)/ (2x + 1) = 17 Since, we have two unknown values and only one equation so the value can’t be determined.Â
Solve the quadratic equations and determine the relation between x and y:
Equation 1: 37x² - 172x + 135 = 0
Equation 2: 29y² - 132y + ...
I. p2 - 19p + 88 = 0Â Â
II. q2 - 48q + 576 = 0
For what real value(s) of k does the quadratic equation - x² − (k + 3)x + 2k = 0, have equal real roots?
I. x2 – 12x + 32 = 0
II. y2 + y - 20 = 0
I. 195x² - 46x - 21 = 0
II. 209y² + 13y - 12 = 0
I. x² - (16)2 = 0
II. 2y - 14 = 0
Solve for x: |2x − 5| + |x + 1| ≤ 10.
I. 9x2 + 45x + 26 = 0
II. 7y2 – 59y − 36 = 0
Roots of the quadratic equation 2x2 + x – 528 = 0 is
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