| "Phrases" Related to Inequalities: |
Let's establish some vocabulary that will be associated with inequalities.
You will most likely run into the phrases listed below when dealing with applications of inequalities. These phrases occur in problems that require the creation of an inequality.
| "Phrases" and Inequalities: |
< |
> |
< |
> |
• less than
• fewer than
• below
• under
|
• greater than
• exceeds
• above
• more than
• over |
• less than or equal to
• maximum
• at most
• no more than
• no greater than
• does not exceed
• up to
• bottom
• at or below |
• greater than or equal to
• minimum
• at least
• no less than
• no fewer than
• no smaller than
• not below
• top
• at or above |
Things to remember when working with word problems:
1. Read carefully.
2. Make sure your answer makes sense.
3. Round appropriately, if needed, based upon the question.
4. Check your answer.
5. If graphing is involved, be sure to limit the domain and range as needed.
Erin bought packages of balloons costing $2.85 per pack and packages of confetti costing $1.95 per pack for a surprise party. Let x = the number of packages of balloons, and y = the number of packages of confetti. If Erin has $35 to spend on these decorations, which inequality models this situation?
1) 2.85x + 1.85y < 35
2) 1.85x + 2.85y< 35
3) 2.85x + 1.85y > 35
4) 1.85x + 2.85y > 35 |
Solution: 1
Be sure the variables agree with the prices.
x is $2.85 and y is $1.95
The most she has to spend is $35, so the totals must be less than or equal to 35.
|
Zander designs cartoon portraits of people's pets. He makes a profit of $50 on each large animal portrait, and $35 on each small animal portrait. Let b = the number of large portraits and s = the number of small portraits. If he wants to make a profit of at least $250 from these sales, write an inequality to represent this situation.
Solution: 50b + 35s > 250
"At least" means 250 or more.
Be sure the variables agree with the prices.
b is $50 and s is $35
|
Kylie has $300 in her savings account. She plans to withdraw $20 a week for lunches. If she wants to keep a minimum of $100 in the account, how many weeks can she continue to withdraw the money?
Solution: Not more than 10 weeks.
"minimum" means $100 or more.
Let w = weeks
300 - 20w > 100
200
> 20w
10
> w |
Raffle tickets for a charity are sold in sets: 1 pack of 4 tickets for $28 and 1 pack of 8 tickets for $54. How many packs of tickets must be sold for the charity to make a profit of no less than $30,000? Show the linear inequality and the graph.
Solution:
Inequality:
x = 4 packs and y = 8 packs
"no less than" means 30,000 or more
28x + 54y > 30,000
Graph:
Graph line 28x + 54y = 30000
Shade only the first quadrant.
It is not possible to sell a negative number
of packs of tickets of either type.
The solution is any ordered pair (x,y) in the shaded yellow region or on the solid line. |
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