ALG 235 | September 12, 2025
Evelyn Ramirez
R. Walker
ALG 235
Algebra Practice Exam
With Solutions
Problem 1: A cell phone plan costs 23.15 per month plus 4.93 per text message. If the total
cost is $258.90, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
258.90 = 23.15 + 4.93x
Solving for x:
258.90 - 23.15 = 4.93x
235.75 = 4.93x
x = 235.75 ÷ 4.93
x = 47.8 text messages
Mathematical justification:
Check: 23.15 + 4.93(47.8) = 23.15 + 235.65 = 258.80 ✓
Problem 2: A cell phone plan costs 88.53 per month plus 4.54 per text message. If the total
cost is $357.79, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
357.79 = 88.53 + 4.54x
Solving for x:
357.79 - 88.53 = 4.54x
269.26 = 4.54x
x = 269.26 ÷ 4.54
x = 59.3 text messages
Verify:
Page
This study source was downloaded by 100000901307859 from CourseHero.com of
on 10-13-2025 00:29:57 GMT -05:00
https://www.coursehero.com/file/251518297/MATH-296-Algebra-Solutions-5785docx/
, ALG 235 | September 12, 2025
Check: 88.53 + 4.54(59.3) = 88.53 + 269.22 = 357.75 ✓
Problem 3: A bacteria culture starts with 347 bacteria and grows exponentially at a rate of
11.0% per hour. Write the exponential function and find the population after 8 hours.
Solution:
Exponential growth model: P(t) = P₀ × (1 + r)^t
P(t) = 347 × (1 + 0.110)^t
P(t) = 347 × 1.110^t
After 8 hours:
P(8) = 347 × 1.110^8
P(8) = 347 × 2.305
P(8) = 800 bacteria
Note: Using the equation we learned in class
Problem 4: A cell phone plan costs 91.20 per month plus 4.58 per text message. If the total
cost is $170.57, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
170.57 = 91.20 + 4.58x
Solving for x:
170.57 - 91.20 = 4.58x
79.37 = 4.58x
x = 79.37 ÷ 4.58
x = 17.3 text messages
Double-checking the work:
Check: 91.20 + 4.58(17.3) = 91.20 + 79.23 = 170.43 ✓
(Similar to homework problem #12)
Note: The textbook example on page 281 shows a similar approach
Page
This study source was downloaded by 100000901307859 from CourseHero.com of
on 10-13-2025 00:29:57 GMT -05:00
https://www.coursehero.com/file/251518297/MATH-296-Algebra-Solutions-5785docx/
Evelyn Ramirez
R. Walker
ALG 235
Algebra Practice Exam
With Solutions
Problem 1: A cell phone plan costs 23.15 per month plus 4.93 per text message. If the total
cost is $258.90, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
258.90 = 23.15 + 4.93x
Solving for x:
258.90 - 23.15 = 4.93x
235.75 = 4.93x
x = 235.75 ÷ 4.93
x = 47.8 text messages
Mathematical justification:
Check: 23.15 + 4.93(47.8) = 23.15 + 235.65 = 258.80 ✓
Problem 2: A cell phone plan costs 88.53 per month plus 4.54 per text message. If the total
cost is $357.79, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
357.79 = 88.53 + 4.54x
Solving for x:
357.79 - 88.53 = 4.54x
269.26 = 4.54x
x = 269.26 ÷ 4.54
x = 59.3 text messages
Verify:
Page
This study source was downloaded by 100000901307859 from CourseHero.com of
on 10-13-2025 00:29:57 GMT -05:00
https://www.coursehero.com/file/251518297/MATH-296-Algebra-Solutions-5785docx/
, ALG 235 | September 12, 2025
Check: 88.53 + 4.54(59.3) = 88.53 + 269.22 = 357.75 ✓
Problem 3: A bacteria culture starts with 347 bacteria and grows exponentially at a rate of
11.0% per hour. Write the exponential function and find the population after 8 hours.
Solution:
Exponential growth model: P(t) = P₀ × (1 + r)^t
P(t) = 347 × (1 + 0.110)^t
P(t) = 347 × 1.110^t
After 8 hours:
P(8) = 347 × 1.110^8
P(8) = 347 × 2.305
P(8) = 800 bacteria
Note: Using the equation we learned in class
Problem 4: A cell phone plan costs 91.20 per month plus 4.58 per text message. If the total
cost is $170.57, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
170.57 = 91.20 + 4.58x
Solving for x:
170.57 - 91.20 = 4.58x
79.37 = 4.58x
x = 79.37 ÷ 4.58
x = 17.3 text messages
Double-checking the work:
Check: 91.20 + 4.58(17.3) = 91.20 + 79.23 = 170.43 ✓
(Similar to homework problem #12)
Note: The textbook example on page 281 shows a similar approach
Page
This study source was downloaded by 100000901307859 from CourseHero.com of
on 10-13-2025 00:29:57 GMT -05:00
https://www.coursehero.com/file/251518297/MATH-296-Algebra-Solutions-5785docx/
