Application of Inequalities

Which inequality matches the story:
Twice a number increased by four is greater than six.

• 2x +4 > 6
• 2x + 4 < 6
• 4x + 2 > 6
• 2x - 4 < 6

Jimmy needs at least $250 to buy 1 ticket to the Cowboys playoff game.  He is raising money by doing yard work.  He charges $20 to mow and trim and $10 to rake up leaves. Which inequality represents the number of yards he needs to mow, x, and the number of yards he needs to rake, y, to attend the game.  

• 20x + 10y ≥ 250
• 20y + 10x ≥ 250
• 30xy ≥ 250
• 20x + 10y ≤ 250

You can’t spend any more than $150 on a road trip.  You figure that you will spend $30 in food and $0.10 per mile in gas.  Which inequality represents the number of miles, x, that you can drive.

• .10x + 30 ≤ 150
• 30x + .10 ≤ 150
• .10x + 30 ≥ 150
• .10 + 30x ≥ 150

Suzy is buying In-N-Out Burger for lunch for her friends.  The hamburgers cost $3.50 each and the drinks cost $1.50 each.  She wants to spend no more than $30 on lunch.  What inequality represents the number of hamburgers, h, and number of drinks, d, that she can buy?

• 3.5h + 1.5d ≤ 30
• 3.5d + 1.5h ≤ 30
• 3.5h + 1.5d ≥ 30
• 3.5h + 1.5d < 30

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10
• 1.75 + 0.65m > 10
• 1.75m + 0.65 < 10
• 1.75m + 0.65 > 10

Keith wants to have at least $300 in his bank account at the end of the summer.  He makes an initial deposit of $100 at the beginning of the summer and then deposits $25 every week.

• 300 < 100 + 25w
• 300 < 100w + 25
• 300 > 100 + 25w
• 300 > 100w + 25

Debbie has at most $175 to spend on clothes.  She wants to buy jeans for $28 each and t-shirts for $12 each.

• 28j + 12t < 175
• 28t + 12j < 175
• 28j + 12t > 175
• 28t + 12j > 175

Brian mailed Christmas presents late to his family.  To send boxes it cost $7.50 each and $0.45 per letter. He can’t spend more than $40 to mail everything.  What inequality represents the number of boxes, B, and letters, L, that he can send?

• 7.50B + 0.45L < 40
• 7.50L + 0.45B < 40
• 7.50B + 0.45L > 40
• 7.50L + 0.45B > 40

Twice a number minus three is greater than 27.

• 2x – 3 > 27
• 2x – 3 < 27
• 3 – 2x > 27
• 3 – 2x < 27

A limo driver needs to make more than $450 in one day.  He charges a rental fee of $375 and $0.85 per mile.  What inequality represents the number of miles, x, he would have to drive to reach his goal?

• 0.85x + 375 > 450
• 0.85x + 375 < 450
• 0.85 + 375x > 450
• 0.85 + 375x < 450