Expert: Sherry Wallin - 7/17/2010

Question
Hello,

Good day to you.

I have three questions, is it possible to answer them for me.

Q1: Write an inequality in the variable x for the degree measure of the smallest angle of the triangle shown in the figure, given that the degree measure of the smallest angle is at most 30°.

Q2: Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. Ronald still owes $11,025 on the car. Ronald must get enough to at least pay off the loan. What is the range of the selling price?

Q3: Professor Williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put Wendy’s average between 70 and 79 inclusive?

Answer
Hi AGA~
   
For #1 I don't see a figure?

#2:  let x = selling price so the commission is .10x = .1x
    Since he owes $11,025 he must get 11,025 + .1(11,025) dollars so the selling price must be at least this much: x > 11,025 + .1(11,025) = 1.1(11,025) this means the range is
[1.1(11025), 00) = (12127.50, 00)

#3:  let x = score on final exam, then you want (2/3)(48) + (1/3)x to be between 70 and 79
which implies 70 <= (2/3)(48) + (1/3)x < = 79  now solve for x in the compound inequality:
multiply first by the greatest common denominator which is 3:
3[70) <= 3(2/3)48 + 3(1/3)x <= 3(79)
210 <= 2(48) + x <= 237
210 <= 96 + x <= 237
-96   -96        -96
114 <= x <= 141 this means that Wendy needs to get between 114% and 141% inclusive in order to get an average score between 70% and 79% inclusive which of course is an impossibility thus the range of scores is the empty set {} or the null set or there is no solution which all mean the same thing.

Math Prof