MATH 235X | September 13, 2025
Ryan Parker
Mark Young
MATH 235X
River Riverside University
Algebra Homework Assignment
With Solutions
Problem 1: A gym membership has an enrollment fee of 93.69 and costs 3.76 per month. If
the total cost is $132.01, find the number of months used.
Solution:
Let x = number of months
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
132.01 = 93.69 + 3.76x
Solving for x:
132.01 - 93.69 = 3.76x
38.32 = 3.76x
x = 38.32 ÷ 3.76
x = 10.2 months
The logic behind this step:
Check: 93.69 + 3.76(10.2) = 93.69 + 38.35 = 132.04 ✓
Problem 2: Given f(x) = 3x + 4 and g(x) = x² - 1, find: a) (f ∘ g)(x) b) (g ∘ f)(x) c) (f ∘ g)(3)
Solution:
Given: f(x) = 3x + 4, g(x) = x² - 1
a) (f ∘ g)(x) = f(g(x)) = f(x² - 1)
= 3(x² - 1) + 4 = 3x² - 3 + 4 = 3x² - -1
b) (g ∘ f)(x) = g(f(x)) = g(3x + 4)
= (3x + 4)² - 1 = 9x² + 24x + 16 - 1 = 9x² + 24x + 15
c) (f ∘ g)(3) = f(g(3)) = f(3² - 1) = f(8)
= 3(8) + 4 = 28
Note: Following the steps we learned for algebra problems
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, MATH 235X | September 13, 2025
Problem 3: Solve the logarithmic equation: log₍10₎(5x - 10) = 2
Solution:
Given: log₍10₎(5x - 10) = 2
Converting to exponential form:
5x - 10 = 10²
5x - 10 = 100
5x = 110
x = 110/5
x = 22.000
Shortcut:
Check: log₍10₎(5(22.000) - 10) = log₍10₎(100) = log₍10₎(10²) = 2 ✓
Problem 4: A bakery has monthly fixed costs of $1900 and variable costs of $1.8 per
pastries. Each pastries sells for $4.5. a) Write the cost function C(x) and revenue function
R(x) b) Find the break-even point c) How much profit is made when 800 pastriess are sold?
d) How many pastriess must be sold to make a profit of $2,000?
Solution:
a) Cost and Revenue Functions:
Cost function: C(x) = 1900 + 1.8x
(Fixed costs + Variable costs per unit × number of units)
Revenue function: R(x) = 4.5x
(Price per unit × number of units)
b) Break-even point:
At break-even: R(x) = C(x)
4.5x = 1900 + 1.8x
4.5x - 1.8x = 1900
2.70x = 1900
x = 1900 ÷ 2.70
x = 704 pastriess
Break-even point: 704 pastriess
c) Profit when 800 pastriess are sold:
Profit = Revenue - Cost
P(800) = R(800) - C(800)
P(800) = 4.5(800) - [1900 + 1.8(800)]
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:44:43 GMT -05:00
https://www.coursehero.com/file/251540569/ALG-201-Algebra-Solutions-6345docx/
Ryan Parker
Mark Young
MATH 235X
River Riverside University
Algebra Homework Assignment
With Solutions
Problem 1: A gym membership has an enrollment fee of 93.69 and costs 3.76 per month. If
the total cost is $132.01, find the number of months used.
Solution:
Let x = number of months
Setting up the equation:
Total Cost = Fixed Cost + Variable Cost
132.01 = 93.69 + 3.76x
Solving for x:
132.01 - 93.69 = 3.76x
38.32 = 3.76x
x = 38.32 ÷ 3.76
x = 10.2 months
The logic behind this step:
Check: 93.69 + 3.76(10.2) = 93.69 + 38.35 = 132.04 ✓
Problem 2: Given f(x) = 3x + 4 and g(x) = x² - 1, find: a) (f ∘ g)(x) b) (g ∘ f)(x) c) (f ∘ g)(3)
Solution:
Given: f(x) = 3x + 4, g(x) = x² - 1
a) (f ∘ g)(x) = f(g(x)) = f(x² - 1)
= 3(x² - 1) + 4 = 3x² - 3 + 4 = 3x² - -1
b) (g ∘ f)(x) = g(f(x)) = g(3x + 4)
= (3x + 4)² - 1 = 9x² + 24x + 16 - 1 = 9x² + 24x + 15
c) (f ∘ g)(3) = f(g(3)) = f(3² - 1) = f(8)
= 3(8) + 4 = 28
Note: Following the steps we learned for algebra problems
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:44:43 GMT -05:00
https://www.coursehero.com/file/251540569/ALG-201-Algebra-Solutions-6345docx/
, MATH 235X | September 13, 2025
Problem 3: Solve the logarithmic equation: log₍10₎(5x - 10) = 2
Solution:
Given: log₍10₎(5x - 10) = 2
Converting to exponential form:
5x - 10 = 10²
5x - 10 = 100
5x = 110
x = 110/5
x = 22.000
Shortcut:
Check: log₍10₎(5(22.000) - 10) = log₍10₎(100) = log₍10₎(10²) = 2 ✓
Problem 4: A bakery has monthly fixed costs of $1900 and variable costs of $1.8 per
pastries. Each pastries sells for $4.5. a) Write the cost function C(x) and revenue function
R(x) b) Find the break-even point c) How much profit is made when 800 pastriess are sold?
d) How many pastriess must be sold to make a profit of $2,000?
Solution:
a) Cost and Revenue Functions:
Cost function: C(x) = 1900 + 1.8x
(Fixed costs + Variable costs per unit × number of units)
Revenue function: R(x) = 4.5x
(Price per unit × number of units)
b) Break-even point:
At break-even: R(x) = C(x)
4.5x = 1900 + 1.8x
4.5x - 1.8x = 1900
2.70x = 1900
x = 1900 ÷ 2.70
x = 704 pastriess
Break-even point: 704 pastriess
c) Profit when 800 pastriess are sold:
Profit = Revenue - Cost
P(800) = R(800) - C(800)
P(800) = 4.5(800) - [1900 + 1.8(800)]
Page
This study source was downloaded by 100000898062787 from CourseHero.com of
on 09-30-2025 22:44:43 GMT -05:00
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