MATH 247 | September 13, 2025
Elijah Hall
Prof. Michelle Campbell
MATH 247
Eastern State Columbia State University
Algebra Quiz Practice
With Solutions
Problem 1: A projectile is fired upward from ground level with initial velocity 37 m/s. The
height equation is h(t) = 37t - 4.9t². Find when it hits the ground and its maximum height.
Solution:
Given: h(t) = 37t - 4.9t²
a) Time to hit ground (h = 0):
37t - 4.9t² = 0
t(37 - 4.9t) = 0
t = 0 (launch) or t = 37/4.9 = 7.55 seconds
b) Maximum height occurs at vertex:
t = -b/(2a) = -37/(2×(-4.9)) = 3.78 seconds
Maximum height:
h(3.78) = 37(3.78) - 4.9(3.78)²
h(3.78) = 69.8 meters
(Similar to homework problem #12)
Problem 2: A rental car costs 88.52 per day plus 4.64 per mile. If the total cost is $306.91,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
306.91 = 88.52 + 4.64x
Solving for x:
306.91 - 88.52 = 4.64x
218.39 = 4.64x
x = 218.39 ÷ 4.64
x = 47.1 miles
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:47:09 GMT -05:00
https://www.coursehero.com/file/251540575/MTH-292P-Algebra-Fall2023-Solutions-8377docx/
, MATH 247 | September 13, 2025
Another way to think about it:
Check: 88.52 + 4.64(47.1) = 88.52 + 218.54 = 307.06 ✓
(Similar to homework problem #12)
Problem 3:
Solution:
Note: I started by identifying this as a algebra problem
Problem 4: A cell phone plan costs 91.61 per month plus 0.97 per text message. If the total
cost is $314.77, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
314.77 = 91.61 + 0.97x
Solving for x:
314.77 - 91.61 = 0.97x
223.16 = 0.97x
x = 223.16 ÷ 0.97
x = 230.1 text messages
Alternative approach:
Check: 91.61 + 0.97(230.1) = 91.61 + 223.20 = 314.81 ✓
Note: I'll need to review this concept before the midterm
Problem 5: A cell phone plan costs 98.07 per month plus 3.54 per text message. If the total
cost is $327.69, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
327.69 = 98.07 + 3.54x
Solving for x:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:47:09 GMT -05:00
https://www.coursehero.com/file/251540575/MTH-292P-Algebra-Fall2023-Solutions-8377docx/
Elijah Hall
Prof. Michelle Campbell
MATH 247
Eastern State Columbia State University
Algebra Quiz Practice
With Solutions
Problem 1: A projectile is fired upward from ground level with initial velocity 37 m/s. The
height equation is h(t) = 37t - 4.9t². Find when it hits the ground and its maximum height.
Solution:
Given: h(t) = 37t - 4.9t²
a) Time to hit ground (h = 0):
37t - 4.9t² = 0
t(37 - 4.9t) = 0
t = 0 (launch) or t = 37/4.9 = 7.55 seconds
b) Maximum height occurs at vertex:
t = -b/(2a) = -37/(2×(-4.9)) = 3.78 seconds
Maximum height:
h(3.78) = 37(3.78) - 4.9(3.78)²
h(3.78) = 69.8 meters
(Similar to homework problem #12)
Problem 2: A rental car costs 88.52 per day plus 4.64 per mile. If the total cost is $306.91,
find the number of miles used.
Solution:
Let x = number of miles
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
306.91 = 88.52 + 4.64x
Solving for x:
306.91 - 88.52 = 4.64x
218.39 = 4.64x
x = 218.39 ÷ 4.64
x = 47.1 miles
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:47:09 GMT -05:00
https://www.coursehero.com/file/251540575/MTH-292P-Algebra-Fall2023-Solutions-8377docx/
, MATH 247 | September 13, 2025
Another way to think about it:
Check: 88.52 + 4.64(47.1) = 88.52 + 218.54 = 307.06 ✓
(Similar to homework problem #12)
Problem 3:
Solution:
Note: I started by identifying this as a algebra problem
Problem 4: A cell phone plan costs 91.61 per month plus 0.97 per text message. If the total
cost is $314.77, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
314.77 = 91.61 + 0.97x
Solving for x:
314.77 - 91.61 = 0.97x
223.16 = 0.97x
x = 223.16 ÷ 0.97
x = 230.1 text messages
Alternative approach:
Check: 91.61 + 0.97(230.1) = 91.61 + 223.20 = 314.81 ✓
Note: I'll need to review this concept before the midterm
Problem 5: A cell phone plan costs 98.07 per month plus 3.54 per text message. If the total
cost is $327.69, find the number of text messages used.
Solution:
Let x = number of text messages
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
327.69 = 98.07 + 3.54x
Solving for x:
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:47:09 GMT -05:00
https://www.coursehero.com/file/251540575/MTH-292P-Algebra-Fall2023-Solutions-8377docx/
