Solving Word Problems in Algebra
Practice Problems
Did you read through the lesson on Inequality Word Problems? Are you ready to practice inequalities by solving these word problems? Yes... I do know the answer by now - but - I know you can do it! Now, I want you to prove it to yourself.
Let's quickly recap a few things and you'll be on your way!
Let's keep these key words for inequalities handy:
Inequality Key Words
- at least - means greater than or equal to
- no more than - means less than or equal to
- more than - means greater than
- less than - means less than
Work through each problem slowly and start by identifying your variables. Then write an inequality that represents the problem.
Once you've written the inequality, the hard work is done and you are ready to solve!
Don't forget to check your answers at the end. This is definitely a habit that you want to set for yourself.
Ok... get to work!
Problem 1
Chris wants to order DVDs over the internet. Each DVD costs $15.99 and shipping for the entire order is $9.99. Chris has no more than $100 to spend.
- Write an inequality that represents Chris' situation.
- How many DVDs can Chris order without exceeding his $100 limit?
Problem 2
Skate Land charges a $50 flat fee for birthday party rental and $5.50 per person. Joann has no more than $100 to spend on the birthday party.
- Write an inequality to represents Joann's situation.
- How many people can Joann invite to her birthday party without exceeding her limit of $100?
Solutions
Problem 1:
Chris wants to order DVDs over the internet. Each DVD costs $15.99 and shipping for the entire order is $9.99. Chris has no more than $100 to spend.
- Write an inequality that represents Chris' situation.
Let d = the number of DVDs purchase
15.99d + 9.99 < 100
(This translates to 15.99 times the number of DVDs + 9.99 shipping cost must be less than or equal to 100 dollars.
- How many DVDs can Chris order without exceeding his limit?
We need to solve:
15.99d + 9.99 < 100
15.99d + 9.99 - 9.99 < 100 - 9.99
15.99d<90.01
15.99 15.99
d < 5.6
Since Chris cannot order 0.6 of a DVD, we must round down to 5.
Chris can order 5 DVDs without exceeding his limit of $100.
Problem 2:
Skate Land charges a $50 flat fee for birthday party rental and $5.50 per person. Joann has no more than $100 to spend on the birthday party.
- Write an inequality to represents Joann's situation.
Let p = the number of people invited to the party
5.50p + 50 < 100
(This translates to $5.50 per person times the number of people plus $50 for the flat fee. This value must be less than or equal to $100.)
- How many people can Joann invite to her birthday party without exceeding her limit?
5.50p + 50 < 100
5.50p + 50 - 50 < 100 - 50
5.50p < 505.50 5.50
p < 9
Joann can invite up to 9 people without exceeding her limit of $100.
Great Job! Keep up the good work!
Now you are ready to move on to Graphing Inequalities
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