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marshall27 [118]
3 years ago
6

Lee and Fred are elementary school teachers. Fred works for a charter school in Pacific Palisades, California, where class size

reduction is a goal for 2013. Lee works for a noncharter school where funds do not allow for class size reduction policies. Lee’s fifth-grade class has 1.0 times as many students as Fred’s. a. If there are a total of 60 students, how many students does Fred’s class have? (Round your answers to the nearest whole number. ) Number of students b. If there are a total of 60 students, how many students does Lee’s class have? (Round your answers to the nearest whole number. ) Number of students
Mathematics
1 answer:
Allushta [10]3 years ago
4 0

Let,

Lee’s class size = L

Fred’s class size = F

 

We are told that Lee’s fifth-grade class has 1.0 times as many students as Fred’s

Therefore, L = 1F

L = F

 

Question A. If there are a total of 60 students, how many students does Fred’s class have? 

Total number of students = 60

L + F = 60

 

Since L = F

L + F = F + F + 60

F + F = 60

2F = 60

F = 60/2

F = 30

Therefore, if there are a total of 60 students, Fred’s class has 30 students.

 

 

QUESTION B. If there are a total of 60 students, how many students does Lee’s class have?

Total number of students = 60

L + F = 60

 

Since L = F

L + F = L + L + 60

L + L = 60

2L = 60

L = 60/2

L = 30

Therefore, if there are a total of 60 students, Lee’s class has 30 students.

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Answers:

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  2. B) No real solutions
  3. C) Two solutions
  4. A) One solution
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Explanations:

  1. Note how (11)^2 = (11)*(11) = 121 and also (-11)^2 = (-11)*(-11) = 121. The two negatives multiply to a positive. So that's why the solution is x = plus/minus 11. The plus minus breaks down into the two equations x = 11 or x = -11.
  2. There are no real solutions here because the left hand side can never be negative, no matter what real number you pick for x. As mentioned in problem 1, squaring -11 leads to a positive number 121. The same idea applies here as well.
  3. The two solutions are x = 0 and x = -2. We set each factor equal to zero through the zero product property. Then we solve each equation for x. The x+2 = 0 leads to x = -2.
  4. We use the zero product property here as well. We have a repeated factor, so we're only solving one equation and that is x-3 = 0 which leads to x = 3. The only root is x = 3.
  5. Apply the FOIL rule on (x+1)(x+17) to end up with x^2+17x+1x+17 which simplifies fully to x^2+18x+17. The middle x coefficient is 18, while the constant term is 17.
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