One Step Inequalities from Word Problems

Your brother has $2,000 saved for a vacation. His airplane ticket is $637. Which inequality can be used to find out how much he can spend on everything else?

• 637 + x ≤ 2000

• x − 637 ≤ 2000

• 637 + x ≥ 2000

• x − 637 < 2000

Trisha and her three sisters to decide to purchase their mom a Christmas gift. They decide that everyone will contribute an equal amount, up to $60 per person. Which inequality will help find how much money will the sisters spend on their mom for Christmas?

• x ÷ 4 ≤ 60

• 4x ≤ 60

• x ÷ 4 ≥ 60

• 4x ≥ 60

A personal trainer charges a one-time fee of $60 plus $25 for each individual session. A fitness club charges a yearly fee of $450 plus $10 for each session with a personal trainer. At what point does it become cheaper to join the gym as opposed to working with only a personal trainer?

Remember there are two sides to every inequality.

• After 26 visits with a trainer.

• After 15 visits with a trainer.

• On the 26th visit.

• It is never cheaper.

Which problem situation can be represented by this inequality?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $22.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $22.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $12.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor purchased a vintage comic book from the store for $95.00 and then purchased c more comic books for $22.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

• Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $22.50 each and then spent $25.00 on a comic book portfolio. Victor purchased a vintage comic book from the store for $95.00 and then purchased c more comic books for $12.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

Which situation can be represented by the inequality 2x + 18 < 3x + 11?

• Tori is on the 18th step from the bottom of a staircase and goes up 3 steps every second. Naoki is on the 11th step from the bottom and goes up 2 steps every second. After how many seconds will Naoki pass Tori?

• Ana has made 18 bracelets and continues to make 2 bracelets each day. Elliot has made 11 bracelets and continues to make 3 bracelets each day. After how many days will Elliot have more bracelets than Ana?

• Gina has $2 in her savings account and adds $18 each week. Hiram has $3 in his savings account and adds $11 each week. After how many weeks will Gina have more money in her savings account than Hiram?

• Dhara has eaten 18 french fries and continues to eat 2 with each bite. Kendrick has eaten 11 french fries and continues to eat 3 with each bite. After how many bites will Dhara have eaten more french fries than Kendrick?

At a fruit stand, each pound of apples has a cost of x dollars. Which situation can be represented by the inequality ?

• The cost of 7 pounds of apples is greater than the cost of 6 bunches of bananas.

• The cost of 7 pounds of apples is $4 greater than the cost of 2 pounds of apples.

• The cost of 7 pounds of apples is greater than the cost of 2 pounds of apples plus a $4 bunch of bananas.

• The cost of 7 pounds of apples is less than the cost of 2 pounds of apples plus a $4 bunch of bananas.

Which situation can be represented by this inequality?

• The cost of 12 concert tickets is greater than the cost of 6 tickets with a $4 discount.

• The cost of 12 concert tickets with a $4 discount is greater than the cost of 6 tickets.

• The cost of 12 concert tickets is less than the cost of 6 tickets with a $4 discount.

• The cost of 12 concert tickets is greater than 4 tickets with a $6 discount.

A movie theater sells tickets for the cost of x dollars. Which situation below can be represented by this inequality?

15x < 12x + 16

• The cost of 15 tickets is greater than the cost of 12 tickets plus $16 for snacks.

• The cost of 15 tickets is less than the cost of 12 tickets plus $16 for snacks.

• The cost of 12 tickets with a coupon for $16 is less than 15 tickets.

• The cost of 15 tickets is $16 greater than the cost of 12 tickets.

Which problem situation can be represented by this inequality?

• Chris and Brooklyn shop at Book Heaven, which offers reward points for each book that is purchased. Book Heaven offers two reward plans for the customer to choose from. Brooklyn has chosen a plan which gives 9.5 points for each book purchased. Chris has chosen a plan which starts the customer with 6.75 points and rewards 14.5 points for each book purchased. How many books, x, would each have to purchase so that Brooklyn’s reward points are greater than or equal to Chris’ total reward points?

• Stephanie and Chol are racing against each other. Since Stephanie is faster, she is giving Chol a 14.5 feet head start. Stephanie can run at a constant rate of 9.5 feet per second, while Chol can run at a constant rate of 6.75 feet per second. How many seconds, x, will Stephanie and Chol be running in the race when Chol’s distance from the starting line is greater than or equal to Stephanie’s distance from the starting line?

• Over the course of a year, Ryan and Tanya donate a portion of their income to charity. Each month, Tanya donates $6.75 to Stars for Children. Ryan donates $14.50 at the beginning of the year to Helping Hands and then donates $9.50 each month to Puppies for Firefighters. After how many months, x, will Ryan’s total charity donations be greater than or equal to Tanya’s total donations?

• Jeff plays an online computer game in which he earns 6.75 coins for each completed challenge. Juliana plays the same online computer game and earns 19.5 coins for each completed challenge. How many challenges, x, will be completed when Jeff has more coins than Juliana?