Modeling Inequalities

Greens are positive, reds are negative. Solve for x

• x<7

• x>7

• x<14

• x<4

Daniel can spend no more than $40 at the fair. If admission into the fair is $10 and the rides cost $1.50 each, which inequality represents the greatest number of rides Daniel can go on?

• 10x + 1.50 ≥ 40

• 1.50x + 10 ≤ 40

• 1.50x + 10 <40

• 10x + 1.50 < 40

Karen has $25 to buy her best friend a gift.  How much can the gift cost?
Let x represent the cost of the gift.

• x > 25

• x ≥ 25

• x < 25

• x ≤ 25

When the temperature falls to -19^oF or below, school is cancelled.  Which inequality shows the temperatures that would close school?

• x > -19

• x ≥ -19

• x < -19

• x ≤ -19

A carpenter has $60 with which to buy supplies. The carpenter needs to buy both nails and screws. Nails cost $12.99 per box, and screws cost $14.99 per box. If n represents the number of boxes of nails and s represents the number of boxes of screws, which of the following systems of inequalities models this situation?

• {12.99n+14.99s $\le$ 60
  
  {n $\ge$ 1
  
  {s $\ge$ 1

Your taxi fare is $2.50 per mile, plus a $5 fee.  You cannot exceed $20.  Which inequality models this scenario?

• 5x + 2.50 ≤ 20

• 2.50x + 5 < 20

• 2.50x + 5 ≤ 20

• 7.50x < 20

Solve for x

• x > 8

• x < 9

• x > 10

• x < 7

Garima likes her job as a baby-sitter (b), but it pays only Rs300 per hour. She has been offered a job as a tutor (t) that pays Rs600 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week, but she needs to make at least Rs6600 per week. Which system of inequalities below correctly models Joann's situation?

• b + t < 15

  3b + 6t > 66

• b + t > 15

  3b + 6t < 66

• 3b + 6t > 15

  b + t < 66

• 300b + 600t < 15

  b + t < 66

Anita is saving for college and wants to take no fewer than $3000 with her for the fall semester. Her summer job pays $9/hour. She has already saved $720. How many hours will Anita have to work during the rest of the summer to meet her goal? Select the inequality that models the situation if h represents the number of hours Anita will need to work.

Kim wants to earn at least $65 from her two jobs next week. At most, she can work 15 hours. Her first job pays $5 per hour, and her second job pays $7 per hour. Let x represent the number of hours worked at the first job and y represent the number of hours worked at the second job. Which system of linear inequalities models Kim's situation?