SAT - Inequalities - chapter 3

If 5r + 7 ≤ 2r − 5, what is the greatest possible value of 2r + 3?

• -5

• -4

• 7

• 11

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

When the stadium, which has seating capacity up to 70,000, opened to the public two hours before the game, there were 35,215 spectators at the stadium. Each minute after, the number of spectators increased by 230. If t represents the time, in minutes, after the stadium opened, which of the following inequalities represents the range of minutes when the stadium is at or above capacity?

• 70,000 − 230 ≤ t

• 70,000 ≤ 230t

• 70,000 − 230t ≥ 35,215

• 35,215 + 230t ≥ 70,000

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

If a point with coordinates (p, q) is a solution to the given system of inequalities, what is the maximum possible value of p?

• 2

• 3

• 5

• 6

Answer explanation

Since p is the x-coordinate, combine the inequalities and determine the maximum value of x.

Combining the two inequalities results in 2x − 4 ≤ y ≤ −x + 5. Since it’s not necessary to know the value of y, drop the middle term and solve for x. Add x to both sides to get 3x − 4 ≤ 5. Add 4 to both sides to get 3x ≤ 9, so x ≤ 3. Either (A) 2 or (B) 3 is an allowable value, but the question asks for the maximum, so (B) is correct.

Alternatively, graph the solution regions in the xy-plane and find that point which is within the common solution region but has the largest x-coordinate.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Malikah is assembling the gear she requires to lead a youth group on a camping trip. She needs to rent some tents and buy some meals-ready-to-eat (MREs). She cannot spend more than $350. Malikah knows that she will need at least 8 tents, which cost $15 each to rent, and 40 MREs, which are priced at $5 each. She knows that she will need at least 5 MREs per tent. Which of the following systems of inequalities represents the limitations above if t is the number of tents and m is the number of MREs?

• 
• 
• 
• 

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Yamen predicts that the winning team of a tournament will score p points. To win a contest, his prediction must be within 3 points of the actual score. If the actual score is a, then which of the following inequalities represents the relationship between p and a required to win the contest?

• |a − p| ≤ 3

• |a − p| ≥ 3

• |a + p| ≤ 3

• |a + p| ≥ 3

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

• I and II only

• I, III, and IV only

• II, III, and IV only

• III and IV only

Answer explanation

Graph the inequalities in the xy plane and find out where the solution region is.

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Joaquin receives a commission of $35 for every desktop computer system that he sells and $25 for every laptop computer. His goals for the month were to sell more than 60 computers and to earn at least $1,600 in commissions. Joaquin exceeded his commission goal, but, fell short of reaching his goal for the number of computers sold. Which of the following systems of inequalities describes the number of desktop computers, d, and laptop computers, p, that Joaquin sold?

• d + p ≤ 59

  35d + 25p > 1, 600

• d + p ≤ 60

  25d + 35p > 1, 600

• d + p ≤ 60

  35d + 25p > 1, 600

• d + p < 60

  35d + 25p ≥ 1, 600

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

What is the minimum value of 5x-1 for the value of x that satisfies the inequality on the left?

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

CCSS.HSA.SSE.A.1

If (0, 0) is a solution to the given system of inequalities, which of the following relationships must be true?

• q > p

• q < p

• |q| > p

• p = -q

Tags

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3

CCSS.HSA.REI.D.12

Maria’s cellular phone company charges $30 per month plus $3 for every gigabyte or portion thereof for data usage. If Maria does not want to spend more than $50 this month, what is the maximum data, in gigabytes, she can use?

• 6

• 7

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.3