Inequalities With Variables on Both Sides Word Problems

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

Which situation best represents the following equation? 8.50x > 1000 + 2.50x

• Jose owns the local Comic Store. He sells comics for $8.50 each. His cost each month is $1,000 plus $2.50 per comic. How many comics, x, must he sell each month to make a profit?

• Jose owns the local Comic Store. He sells comics for $2.50 each. His cost each month is $1,000 plus $8.50 per comic. How many comics, x, must he sell each month to make a profit?

• Jose owns the local Comic Store. He sells comics for $2.50 each. His cost each month is $1,000 plus $2.50 per comic. How many comics, x, must he sell each month to make a profit?

• Jose owns the local Comic Store. He sells comics for $8.50 each. His cost each month is $1,000. How many comics, x, must he sell each month to make a profit?

Which inequality can be represented by the inequality 20x + 50 < 25x

• Greg has $50 in his savings account. He deposits $20 in the account each week. His sister, Lauren opened an account today and will deposit $25 in the account each week. How many weeks will it take for Greg to have more money saved than Lauren?

• Greg has $50 in his savings account. He deposits $20 in the account each week. His sister, Lauren opened an account today and will put $25 in the account each week. How many weeks will it take for Lauren to have more money saved than Greg?

• Greg saves $20 each week to put in his savings account at the bank. His sister, Lauren has saved $50 and will save $25 each week. How many weeks will it take for Greg to have more money than Lauren?

• Greg has saved $50 and plans to put $25 each week in his savings account at the bank. His sister, Lauren has also saved $50 but will put $20 in her bank account each week.

Karissa is going water skiing. She can purchase skis for $125 or she can rent skis for $30 an hour. In both cases she must rent a safety flotation device to wear that is $5 per hour. Which inequality shows the number of hours Karissa must ski for the cost of buying skis to be less than renting skis?

• 125 + 5x > 30x

• 125 + 5x < 35x

• 125 + 5x < 30x

• 125 + 5x > 35x

Kaylee can make $24 per hour by tutoring. Quinn can make $18 per hour by tutoring. Kaylee already has $10. Quinn already has $40. How many hours, x, would it take Kaylee to have a greater amount of money than Quinn?

​ (a)   X ​ (b)   ​ (c)   ​ (d)   X ​ (e)  

< or > or =

• 24

• +10

• >

• 18

• +40

• <

• -24

• -10

• -18

• -40

Cody’s Gym charges a $18 fee to join and $30 per month. Tyler’s Gym charges a $50 fee to join and $20 per month.

Use an inequality to determine how many months will you have to go to the gym before Tyler’s gym becomes the better deal.

• 3

• 4

• 5

• 6

• x ≥ 2
• x ≥ -2
• x ≤ 2
• x ≤ -2

• n < 1
• n < -1
• n > 1
• n > -1

• m < 6
• m < -6
• m > 6
• m > -6

Mona is ordering cups for her school.  Company A charges $3.50 for each cup and a one-time starter fee of $14.  Company B charges $0.50 for each trophy and a one-time starter fee of $22.  
Which inequality can be used to find x, the minimum number of cups that can be ordereed so that the total charge at Company A is less than the total charge at Company B?

• 3.5x + < 0.5x + 22

• 3.5x + 14 > 0.5x + 22

• 3.5 + 14x < 0.5 + 22x

• 3.5 + 14x > 0.5 + 22x