Hello all, I have a short time frame to finish and urgently need help on these 2 problems.
1 answer:
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Given:
Total number of students at Colfax Middle School = 270
Ratio of boys to girls is 5:4.
Total number of students at Winthrop Middle School = 180
Ratio of boys to girls is 4:5.
The two schools hold a dance and all students from both schools attend.
To find:
The fraction of the students at the dance are girls
Solution:
There are 270 students at Colfax Middle School, where the ratio of boys to girls is 5:4.
Number of boys
Number of girls
There are 180 students at Winthrop Middle School, where the ratio of boys to girls is 4:5.
Number of boys
Number of girls
Now,
Total number of students in both schools
Total number of girls in both schools
The fraction of the students at the dance are girls is
Therefore, the required fraction is .
Answer:
2 solutions
Step-by-step explanation:
I like to use a graphing calculator to find solutions for equations like these. The two solutions are ...
- x = 1
- x = 4
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To solve this algebraically, it is convenient to subtract 2x-7 from both sides of the equation:
3x(x -4) +5 -x -(2x -7) = 0
3x^2 -12x +5 -x -2x +7 = 0 . . . . . eliminate parentheses
3x^2 -15x +12 = 0 . . . . . . . . . . . . collect terms
3(x -1)(x -4) = 0 . . . . . . . . . . . . . . . factor
The values of x that make these factors zero are x=1 and x=4. These are the solutions to the equation. There are two solutions.
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<em>Alternate method</em>
Once you get to the quadratic form, you can find the number of solutions without actually finding the solutions. The discriminant is ...
d = b^2 -4ac . . . . where a, b, c are the coefficients in the form ax^2+bx+c
d = (-15)^2 -4(3)(12) = 225 -144 = 81
This positive value means the equation has 2 real solutions.
