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.

Problem 9 :

The graphs show the height restrictions h (in inches) for two rides at an amusement park. Write an inequality that represents the height restriction of each ride.

Solution :

By observing the graph of ride A, we have closed circle and by observing all the values in the shaded region the values are 50, 52, ....... which are greater than 48.

Since we have filled circle, we have to use greater than or equal sign.

h ≥ 48

By observing the graph of ride B, we have unfilled circle and by observing all the values in the shaded region the values are 50, 48 ....... which are lesser than 48.

Since we have unfilled circle, we have to use lesser than or equal sign.

h < 52

Problem 10 :

The winner of a weight-lifting competition bench-pressed 400 pounds. The other competitors all bench-pressed at least 23 pounds less.

a. Write an inequality that represents the weights that the other competitors bench-pressed.

b. Was one of the other competitors able to bench-press 379 pounds? Explain.

Solution :

The winner bench-pressed 400 pounds. The other competitors pressed "at least 23 pounds less." To find the maximum weight another competitor could have lifted, subtract the minimum difference from the winner's total:

400 - 23 = 377

This means the highest weight any other competitor could have lifted is 377 pounds. 

Let w represent the weight bench-pressed by any other competitor. Since their weight must be 377 pounds or lower, we use the "less than or equal to" symbol:

w ≤ 377

Problem 11 :

The graph represents the known melting points of all metallic elements (in degrees Celsius).

a. Write an inequality represented by the graph.

b. Is it possible for a metallic element to have a melting point of −38.87°C? Explain.

Solution :

a) By observing the graph, the values which are lesser than -38.87

x ≤ -38.87

b) -38.87°C is the melting point since it is solution.