SAT Math: Practice Questions-Heart of algebra-Linear inequality word problems

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Question

Sanjay works as a teacher’s assistant for \($\)20 per hour and tutors privately for \($\)25 per hour. Last week, he made at least \($\)100 working \(x\) hours as a teacher’s assistant and \(y\) hours as a private tutor. Which of the following inequalities models this situation?

  1. \(4x+5y \geq 25\)
  2. \(4x+5y \geq 20\)
  3. \(5x+4y \geq 25\)
  4. \(5x+4y \geq 20\)
Answer/Explanation

Ans: B

Question

The 2017 Wyoming state senate had 30 elected members consisting of Democrats and Republicans. Let \(d\) represent the number of Democrats who vote yes for a bill, and let \(r\) represent the number of Republicans who vote yes for a bill. For a bill to pass, more than half of the 30 senators must vote yes. Which of the following inequalities represents all possible values of \(d\) and \(r\) for a bill to pass? 

  1. \(d + r > 15\)
  2. \(d + r < 15\)
  3. \(d + r \geq 15\)
  4. \(d + r \leq 15\)
Answer/Explanation

Ans: A

Question

The solution to which system of inequalities is represented by the shaded region of the graph? 

  1. \(y \leq 7\)
    \(y \leq 2x+1\)
  2. \(y \leq 7\)
    \(y \geq 2x+1\)
  3. \(x \leq 7\)
    \(2y \leq x\)
  4. \(x \leq 7\)
    \(2y \geq x\)
Answer/Explanation

Ans: B

Question

Aracely can spend up to a total of \($\)20 on streamers and balloons for a party. Streamers cost \($\)1.49 per pack, and balloons cost \($\)4.39 per pack. Which of the following inequalities represents this situation, where \(s\) is the number of packs of streamers Aracely can buy, and \(b\) is the number of pack of balloons Aracely can buy? (Assume there is no sales tax.) 

  1. \(1.49s-4.39b\leq 20\)
  2. \(1.49s+4.39b\leq 20\)
  3. \(1.49s-4.39b\geq 20\)
  4. \(1.49s+4.39b\geq 20\)
Answer/Explanation

Ans: B

Question

The coordinates of points \(A\),\(B\) and \(C\) are shown in the \(xy\)-plane above. For which of the following inequalities will each of the points \(A\),\(B\) and \(C\) be contained in the solution region? 

  1. \(y>-x-2\)
  2. \(y\geq -x\)
  3. \(y<x+3\)
  4. \(x<3\)
Answer/Explanation

Ans: A

Question

\(T(n)=80+n\)
\(S(n)=1,280+30n\)

The given equations model the number of teachers and students in a high school from 2002 through 2017. In the equations, \(n\) is the number of years after 2002, where \(n\) is a whole number less than or equal to 15. The predicted number of teachers and students are \(T(n)\) and \(S(n)\), respectively.

Based on the model, what is the first year in which the predicted number of teachers will be greater than 90? 

  1. 2014
  2. 2013
  3. 2012
  4. 2011
Answer/Explanation

Ans: B

Question

A certain elephant weighs 200 pounds at birth and gains more than 2 but less than 3 pounds per day during its first year. Which of the following inequalities represents all possible weights \(w\), in pounds, for the elephant 365 days after its birth? 

  1. \(400<w<600\)
  2. \(565<w<930\)
  3. \(730<w<1,095\)
  4. \(930<w<1,295\)
Answer/Explanation

Ans: D

Question

\(y\)>4\(x\)

\(y\)<-\(x\)

When graphed in the \(xy\)-plane, what point (\(x\), \(y\)) is a solution to the given system of inequalities?

  1. (1,1)
  2. (-2,-2)
  3. (3,-3)
  4. (-4,4)
Answer/Explanation

Ans: B

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