WRITING ONE STEP INEQUALITIES FROM WORD PROBLEMS AND SOLVE

Problem 1 :

Jacob weights more than 50 pounds more than his younger brother, Jared. Jared weighs 46 pounds.

Solution :

Let x be the weight of Jacob.

Weight of Jared = 46 pounds

Weight of Jacob x > 56 + 40

x > 96

Problem 2 :

Analice is 16 years old. If you add together Analice's age and her cousin, Emily's age together you will get more than 31 years.

Solution :

Age of Analice = 16

Age of her cousin Emily = x

16 + x > 31

x > 31 - 16

x > 15

So, the age of Emily will be greater than 15.

Problem 3 :

Bracelets cost $3 each. Rachel can spend no more than $20. How many bracelets can he buy ?

Solution :

Let x the number of bracelets he can buy.

3x ≥ 20

x ≥ 20/3

x ≥ 6.6

So, maximum number of bracelets he can buy is 6.

Problem 4 :

Max earns $9 per hour. This week he is hopping to earn at least $200. How many hours would he need to work ?

Solution :

Amount he is earning per hour = $9

Let x be the number of hours he is working.

He wants to earn atleast 200, then more than 200 is also fine.

9x ≥ 200

x ≥ 200 / 9

x ≥ 22.22

So, he needs to work at least 22 hours.

Problem 5 :

James has $32. He starts shoveling driveways and earns $7 per driveway. He needs at least $75 to buy a skateboard he wants. How many driveways does he need to shovel ?

Solution :

The initial amount James has = 32

He earns $7 per driveway. 

Let x be the number of hours he need to shovel.

32 + 7x ≥ 75

7x ≥ 75 - 32

7x ≥ 43

x ≥ 43/7

x ≥ 6.14

So, the minimum number of hours to work is 6.

Problem 6 :

The seventh grade class is putting on a variety show to raise money. It cost $700 to rent the banquet hall that they are going to use. If they charge $15 for each ticket, how many tickets do they need to sell in order to raise at least $1000?

Solution :

Let x be the number of tickets.

Rent = 700

700 + 15x ≥ 1000

15x ≥ 1000 - 700

15x ≥ 300

x ≥ 300/15

x ≥ 20

So, the minimum number of tickets is 20.

Problem 7 :

Kevin has $25. MP3 downloads cost $0.75 each. How many songs can he download and still have $13 left to spend?

Solution :

Amount he had at the beginning = 25

Number of songs he can download be x

25 - 0.75x ≤13

-0.75x ≤ 13 - 25

-0.75x ≤ -12

x ≤ 12/0.75

x ≤ 16

So, the maximum number of songs he can download is 16.

Problem 8 :

Triniti had $500 in a saving account at the beginning of the summer. She wants to have at least $200 in the account by the end of the summer. She withdraws $25 each week for food, clothes, and movie tickets.

Solution :

Amount Triniti has at the beginning = 500

Minimum amount he should have = 200

Amount withdraws each week = 25

Let x be the number of weeks.

500 - 25x ≥ 200

-25x ≥ 200 - 500

-25x ≥ -300

x ≤ 300/25

x ≤ 12

So, the required number of weeks is 12.