SOLVING ONE STEP INEQUALITIES WORD PROBLEMS

Problem 1 :

Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account?

Solution :

Let number of weeks he is withdrawing be x.

Amount should have atleast 200. So, ≤ 200

Amount he has at the beginning = 500

500 - 25x ≤ 200

Solving for x, we get

-25x ≤ 200 - 500

-25x ≤ -300

Dividing by -25 on both sides, we get

x ≥ 300/25

x ≥ 12

So, the number of weeks he can withdraw the amount is 12 weeks.

Problem 2 :

A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel?

Solution :

Let x be the additional number of mile.

Charge per mile = 0.65

Initial charge = 1.75

At most 10, which is ≤ 10

1.75 + 0.65x ≤10

Subtracting 1.75 on both sides

0.65x ≤10 - 1.75

0.65x ≤ 8.25

x ≤ 8.25/0.65

x ≤ 12.69

So, not more than 12.7 miles.

Problem 3 :

Chris wants to order DVD's over the internet. Each DVD costs $15.99 and shipping the entire order costs $9.99. If he can spend no more than $100, how many DVD's could he buy?

Solution :

Cost of each DVD = $15.99

Order cost = $9.99

He can spend no more than $100, then ≤ 100.

Let x be the number of DVD's.

15.99 x + 9.99 ≤ 100

15.99 x ≤ 100 - 9.99

15.99x ≤ 90.01

x ≤ 90.01/15.99

x ≤ 5.629

The maximum number of DVD's is 5.

Problem 4 :

Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal?

Solution :

Let x be the required number of sessions.

Duration of each session = 0.75 hours

0.75x + 3 ≥ 12

0.75 x  ≥ 12 - 3

0.75 x ≥ 9

x ≥ 9 / 0.75

x ≥ 12

So, 12 hours is the minimum number of hours.

Problem 5 :

Pet Supplies makes a profit of $5.50 per bag on its line of natural dog food. If the store wants to make a profit of no less than $5225, how many bags of dog food does it need to sell?

Solution :

Profit should be no less than $5225, then ≥ 5225

Number of dog food to be sold be x

Profit per bag = 5.50

5.50x ≥ 5225

x ≥ 5225 / 5.50

x ≥ 950

At least 950 bags.

Problem 6 :

Ryan is a wrestler trying to make weight. He currently weighs 200 lbs. If he cuts 2 lbs. per week, how many weeks will it take him to weigh less than 175 lbs.?

Solution :

Let x be the number of weeks he needs to take him to weight less  than 175.

Current weight = 200 lbs

200 - 2x < 175

Subtracting 200 on both sides.

-2x < 175 - 200

-2x < -25

To solve for x, we have to divide by -2 on both sides. Then we have to flip the inequality sign.

x > 25/2

x > 12.5

So, he needs more than 12.5 weeks.

Problem 7 :

Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?

Solution :

There are two schemes :

Membership and non membership.

Let x be the number of times they are using the gym.

Charges for membership = 135 + 2x

Charges for non membership = 11 x

membership should be cheaper than non membership.

135 + 2x < 11x

135 < 11x - 2x

135 < 9x

Dividing by 9 on both sides

135/9 < x

15 < x

x > 15

When the person is using the gym atleast 15 times, the membership would be cheaper.