1. LINEAR INEQUALITY WORD PROBLEMS
ONE VARIABLE

2. EXAMPLE 1
Bill wants to spend less than $26 on a magazine and 5 composition books. The magazine cost $4. Find the maximum cost for each composition book.
c = cost per composition book
Total: 5c (set up same way as an equation)
5c + 4 < 26
5c < 22
c < 4.40
The maximum cost of a composition book is $4.40

3. EXAMPLE 2
Amanda wanted to go climbing at an indoor rock gym. They charge $6 for shoe rental and $8 and hour. If Amanda doesn’t want to pay more than $40 and she needs to rent shoes, how many hours can she climb if you can only pay for whole hours.
h = number of hours
Total: 8h + 6
8h + 6 ≤ 40
8h ≤ 34
h ≤ 4.25
Amanda can climb for at most 4 hours.

4. EXAMPLE 3
More than 450 students went on a field trip. Ten buses were filled and 5 more students traveled in a car. Find the minimum number of students on each bus.
s = number of students
Total : 10s (set up same way as an equation)
10s + 5 > 450
10s > 445
s > 44.5
Can you have ½ a student?
Number of students must be greater than 45.

5. EXAMPLE 4
Elisa won 40 lollipops playing basketball at the school fair. She gave away two to every student in her math class. She has at least 7 left. Find the maximum number of students in her math class.
s = number of students
Difference: 40 – 2s
40 – 2s ≥ 7
– 2s ≥ -33
s ≤ 16.5
There are at most 16 students in her math class

6. EXAMPLE 5
Joe received $3000 in student loans for his first semester of college. He needed to immediately set aside half of that for his rent. With the remaining amount he was planning on buying a laptop for $500 and withdrawing $50 every week for groceries. What is the maximum number of weeks Joe can withdraw money for food?
w = number of weeks
3000/2 = total: w
w ≤ 1500
50w ≤ 1000
w ≤ 20
He can withdrawal money for up to 20 weeks.

7. EXAMPLE 6
To get a nursing degree, Brett needs to get a C in college statistics. His grade is based off of 5 exams. On the first 4 exams Brett scored an 82, 67, 75 and 66. What score does Brett need to get on his last exam to get at least a 73%, the minimum grade for a C?
x = grade on last exam
Mean = sum of all scores / number of exams
sum of all scores: x = x
Mean: (290 + x)/5
(290 + x)/5 ≥ 73
290 + x ≥ 365
x ≥ 75
Brett needs to get at least a 75% to get a “C” in the class.

8. EXAMPLE 7
Ms. Jeffrey is considering 2 bakeries for her wedding. Jane’s Cakes charges a $65 delivery fee and $1.50 per cupcake. Bella’s Cakes charges no delivery fee but charges $3 per cupcake. How many cupcakes would Ms. Jeffrey have to order for Jane’s Cakes to be a better value?
c = number of cupcakes
cost at Jane’s: 1.50c + 65
cost at Bella’s: 3c
1.50c + 65 < 3c
65 < 1.50c
43.3 < c
Ms. Jeffrey must order at least 44 cupcakes.