Math 1324 Homework Answers: Worked Examples & Step-by-Step Solutions for Every Topic

You’re taking Math 1324 — Mathematics for Business and Social Sciences — and the homework is due soon. Maybe tonight. You’ve been staring at a problem about compound interest or linear programming for twenty minutes, and the textbook explanation reads like it was written for someone who already knows the answer.

This guide exists to fix that. Below, you’ll find clear, step-by-step breakdowns for every major problem type you’ll encounter in Math 1324 homework assignments. We’re covering linear functions and depreciation, systems of equations, matrices, linear programming, the mathematics of finance, and probability — basically the entire course, organized the way homework is actually assigned.

This isn’t a cheat sheet. It’s something more useful: a resource that helps you understand how to work through each problem so you can handle the ones on your exam, too.

What Math 1324 Actually Covers (And Why It’s Structured This Way)

Math 1324 is a core curriculum math course offered at virtually every public college and university in Texas. It goes by several names — Finite Mathematics, Mathematics for Business and Social Sciences, Introductory Mathematics for Business — but the content is standardized across institutions through the Texas Higher Education Coordinating Board.

The course is designed for non-STEM majors, particularly students pursuing business, economics, or social science degrees. It covers the mathematical tools that actually show up in those fields: analyzing costs and profits with linear models, optimizing resource allocation with linear programming, computing loan payments and investment growth with finance formulas, and assessing risk with probability.

Here’s the typical topic sequence and how homework is usually organized:

Unit	Core Topics	Common Homework Problem Types
1	Linear Equations & Functions	Depreciation, break-even analysis, cost/revenue/profit
2	Systems of Equations & Matrices	Solving 2×2 and 3×3 systems, matrix operations
3	Linear Programming	Graphing feasible regions, finding optimal values
4	Mathematics of Finance	Simple/compound interest, annuities, present/future value
5	Sets & Counting	Venn diagrams, permutations, combinations
6	Probability & Statistics	Probability distributions, expected value, variance

Let’s work through each one.

Unit 1: Linear Functions, Depreciation, and Break-Even Problems

This is where Math 1324 homework typically starts, and these problems show up on almost every first exam.

Linear Depreciation

The setup is always the same: an asset has an initial value, a useful life in years, and a scrap value (often $0). You need to find the annual depreciation rate and write a value function.

How to solve it:

The annual depreciation rate is calculated by taking the difference between the original cost and the scrap value, then dividing by the number of years. Express this as a negative number because the asset loses value each year.

The value function follows the form V(t) = (depreciation rate) × t + (original cost).

Worked example: A $3,000,000 building is depreciated linearly over 15 years. Scrap value is $0.

• Annual depreciation = (0 − 3,000,000) / 15 = −$200,000 per year
• V(t) = −200,000t + 3,000,000
• Value at year 10: V(10) = −200,000(10) + 3,000,000 = $1,000,000

The key thing students miss: the depreciation rate is negative because the value decreases. If your answer choices show both positive and negative versions, pick the negative one for the rate and make sure the function starts at the original cost (the y-intercept).

Break-Even Analysis

Break-even problems give you a fixed cost, a variable cost per unit, and a selling price per unit. You need the break-even point — where revenue equals cost.

The formulas:

• Cost function: C(x) = (fixed costs) + (variable cost per unit) × x
• Revenue function: R(x) = (selling price per unit) × x
• Profit function: P(x) = R(x) − C(x)
• Break-even: set C(x) = R(x) and solve for x

Worked example: Fixed costs are $27,500. Each phone charger costs $3.50 to produce and sells for $12.00.

• C(x) = 27,500 + 3.50x
• R(x) = 12x
• Break-even: 27,500 + 3.50x = 12x → 27,500 = 8.50x → x ≈ 3,236 units
• Break-even point: (3,236, $38,832)

For profit at a specific production level, just plug into P(x) = 12x − (27,500 + 3.50x) = 8.50x − 27,500.

Unit 2: Systems of Linear Equations and Matrices

Solving Systems of Equations

Math 1324 focuses on two methods: substitution/elimination for 2×2 systems and Gauss-Jordan elimination (row reduction) for larger systems.

For 2×2 systems, most homework problems are straightforward — isolate one variable and substitute. Where students get tripped up is interpreting the results: a single solution means the lines intersect, no solution means they’re parallel, and infinitely many solutions means they’re the same line.

Matrix Operations

Matrix homework typically involves three operations: addition, scalar multiplication, and matrix multiplication. The critical rule for multiplication: the number of columns in the first matrix must equal the number of rows in the second.

Matrix multiplication step-by-step: To find entry (i, j) in the product, take row i of the first matrix and column j of the second matrix, multiply corresponding entries, and add them up.

For a 2×2 example:

If A = [[2, 3], [1, 4]] and B = [[5, 1], [0, 2]], then AB:

• Entry (1,1): 2(5) + 3(0) = 10
• Entry (1,2): 2(1) + 3(2) = 8
• Entry (2,1): 1(5) + 4(0) = 5
• Entry (2,2): 1(1) + 4(2) = 9

Result: [[10, 8], [5, 9]]

Remember: AB ≠ BA in general. Order matters.

Unit 3: Linear Programming

This is the unit that generates the most homework questions — and the most confusion. Linear programming problems ask you to maximize or minimize an objective function subject to constraints.

The Graphical Method (Step by Step)

1. Identify the variables. Usually x and y, representing quantities of two products or resources.
2. Write the constraints as linear inequalities.
3. Graph each constraint. Treat each inequality as an equation first, plot the line, then shade the correct side.
4. Find the feasible region — the area where all shaded regions overlap.
5. Identify the corner points of the feasible region. Solve systems of equations where boundary lines intersect.
6. Evaluate the objective function at each corner point.
7. The optimal value is the largest (for max) or smallest (for min) result.

Worked example:

Maximize C = 2x + 10y subject to:

• 5x + 2y ≤ 40
• x + 2y ≤ 20
• x ≥ 2
• y ≥ 0

Finding the corners: solve the boundary equations pairwise. The feasible region corners are (2, 0), (2, 9), (5, 7.5), and (8, 0).

Evaluate C at each:

• C(2, 0) = 4 + 0 = 4
• C(2, 9) = 4 + 90 = 94
• C(5, 7.5) = 10 + 75 = 85
• C(8, 0) = 16 + 0 = 16

Maximum value: C = 94 at (2, 9).

The most common mistake: forgetting a constraint when finding corners, or mixing up which intersections are actually inside the feasible region. Always verify that each corner point satisfies every constraint.

Unit 4: Mathematics of Finance

Finance problems make up a significant portion of Math 1324 homework, and they rely on correctly identifying which formula to use. Here’s the decision framework.

Identifying the Problem Type

If the problem involves…	It’s a…	Formula
One lump sum growing over time	Future Value (compound interest)	FV = P(1 + r/n)^(nt)
Finding what a future amount is worth today	Present Value (compound interest)	PV = FV / (1 + r/n)^(nt)
Regular equal payments building a fund	Future Value of Annuity	FV = PMT × [(1 + r/n)^(nt) − 1] / (r/n)
Regular equal payments paying off a debt	Present Value of Annuity	PV = PMT × [1 − (1 + r/n)^(−nt)] / (r/n)
A one-time investment at flat rate	Simple Interest	A = P(1 + rt)

Compound Interest: The Details That Matter

Compounding frequency changes everything. The variable n represents how many times per year interest compounds:

• Annually: n = 1
• Semiannually: n = 2
• Quarterly: n = 4
• Monthly: n = 12
• Daily: n = 365

Worked example: $25,000 invested at 2.5% for 35 years, compounded semiannually.

• FV = 25,000(1 + 0.025/2)^(2 × 35)
• FV = 25,000(1.0125)^70
• FV = 25,000(2.38568…)
• FV ≈ $59,642.11

Students lose points by entering r as 2.5 instead of 0.025, or by forgetting to multiply t by n in the exponent. Double-check your calculator entry.

Annuities

If money is deposited or paid at regular intervals, you’re dealing with an annuity. The key distinction: a sinking fund builds up money (future value of annuity), while a loan amortization pays down a debt (present value of annuity).

Unit 5: Sets and Counting Techniques

Venn Diagrams

Venn diagram problems give you information about overlapping sets and ask you to find specific regions. The strategy: start from the innermost region (the intersection of all sets) and work outward.

For two sets A and B within a universal set U, there are four regions:

• A only (in A but not B)
• B only (in B but not A)
• A ∩ B (in both)
• Neither (outside both, still in U)

Permutations vs. Combinations

This distinction drives a huge number of homework questions:

• Permutations (order matters): P(n, r) = n! / (n − r)!
• Combinations (order doesn’t matter): C(n, r) = n! / [r!(n − r)!]

Quick test: If rearranging the selected items creates a different outcome, use permutations. If the group is the same regardless of order, use combinations.

The Multiplication Principle

If one event can happen in m ways and a second event can happen in n ways, both events together can happen in m × n ways. This is the foundation for problems about license plates, code words, and menu selections.

Example: 4 pens used 5 days a week with replacement — that’s 4^5 = 1,024 different sequences.

Unit 6: Probability and Expected Value

Basic Probability

P(event) = (number of favorable outcomes) / (total number of outcomes)

For combined events:

• P(A or B) = P(A) + P(B) − P(A and B)
• P(A and B) = P(A) × P(B) only if A and B are independent

Expected Value and Variance

Expected value is the weighted average of all possible outcomes. This shows up constantly on Math 1324 exams.

Formula: E(X) = x₁p₁ + x₂p₂ + … + xₙpₙ

Variance: Var(X) = Σ pᵢ(xᵢ − μ)², where μ is the expected value.

Worked example:

x	−3	−1	1	3	5
P(X = x)	0.17	0.28	0.15	0.27	0.13

E(X) = (−3)(0.17) + (−1)(0.28) + (1)(0.15) + (3)(0.27) + (5)(0.13) = 0.82

Var(X) = 0.17(−3 − 0.82)² + 0.28(−1 − 0.82)² + 0.15(1 − 0.82)² + 0.27(3 − 0.82)² + 0.13(5 − 0.82)² ≈ 6.9676

The expected value tells you the long-run average outcome. The variance tells you how spread out the outcomes are around that average.

Myth vs. Fact: Common Math 1324 Misconceptions

Myth: You can just memorize formulas and pass. Fact: Math 1324 exams test application, not recall. You’ll get a formula sheet — the challenge is recognizing which formula fits which scenario.

Myth: Linear programming problems always have a single optimal solution. Fact: Sometimes the optimal value occurs along an entire edge of the feasible region, meaning there are infinitely many optimal solutions. This happens when the objective function is parallel to a constraint boundary.

Myth: Compound interest and simple interest give similar results for short time periods. Fact: For short periods at low rates, the difference is small. But over 20+ years, compound interest dramatically outpaces simple interest — which is exactly why the course teaches both.

Myth: Matrix multiplication works just like regular multiplication (order doesn’t matter). Fact: Matrix multiplication is not commutative. AB and BA are generally different matrices, and one may not even be defined when the other is.

A Note on How to Actually Study This Material

Having tutored students through this course across multiple semesters, the single biggest predictor of success isn’t mathematical talent — it’s problem identification. Most Math 1324 problems follow recognizable patterns. Once you can look at a word problem and say “this is a future value of annuity problem” or “this is asking me to find the corners of a feasible region,” you’re 80% of the way to the answer.

Here’s what works: after reading through the explanations above, try solving the practice problems from your textbook without looking at the solutions. When you get stuck, come back and reference the specific section. The goal is to build the reflex of recognizing problem types, not to memorize solutions to specific questions.

If you’re using MyMathLab, CASA CourseWare, or a similar online homework platform, take advantage of the “similar problem” feature. Solving three variations of the same problem type does more for your understanding than reading ten pages of explanation.

FAQ: Math 1324 Homework Questions

What textbook is used for Math 1324?

The most common textbook is Finite Mathematics with Applications by Lial, Hungerford, Holcomb, and Mullins, published by Pearson. Some schools use Mathematical Applications for the Management, Life, and Social Sciences by Harshbarger and Reynolds. Both cover the same core topics — the section numbers just differ.

Is Math 1324 harder than College Algebra?

Math 1324 covers different material, not necessarily harder material. College Algebra focuses on algebraic manipulation and graphing techniques. Math 1324 applies simpler algebra to business-oriented problems — finance, optimization, and probability. Most students find it more manageable once they adjust to the word-problem-heavy format.

Can I use a calculator on Math 1324 exams?

Most instructors require a TI graphing calculator (typically TI-83 or TI-84). Some sections allow the TI-Nspire. Check your syllabus — calculator policies vary by instructor, and some exams restrict calculator use on certain sections.

How is Math 1324 homework graded?

At most Texas colleges, online homework (through MyMathLab, CASA, or a similar platform) counts for no more than 25% of the total course grade. Proctored exams make up at least 70%. Homework is typically auto-graded by the platform, with unlimited attempts on practice and limited attempts on graded assignments.

What’s the difference between Math 1324 and Math 1325?

Math 1324 covers finite mathematics (linear programming, matrices, finance, probability). Math 1325 is Business Calculus, which covers limits, derivatives, and integrals applied to business contexts. Math 1324 is often a prerequisite for Math 1325.

How do I know which finance formula to use?

Ask two questions: (1) Is there a single lump sum or a series of regular payments? (2) Am I finding what money grows to (future value) or what a future amount is worth now (present value)? The answers to those two questions point directly to the correct formula. See the identification table in the Finance section above.

Moving Forward

Math 1324 covers a surprisingly practical set of tools. Linear programming shows up in supply chain optimization. The finance formulas are exactly what banks use to calculate your car loan payment. Probability and expected value underpin every insurance policy and investment decision.

If you’re working through homework right now, start with whichever unit you’re currently covering and use the worked examples as models. If you’re reviewing for an exam, the table at the top of this article maps each unit to its problem types — use it as a checklist.

For additional practice beyond your textbook, Khan Academy covers many of these topics under their “Linear Algebra” and “Statistics and Probability” sections, and Professor Leonard’s YouTube channel offers clear video walkthroughs of finance math and matrix operations.

The homework isn’t the finish line — the exam is. Use this guide to understand the process, and the answers will follow.

ALSO READ: Master The Grill: Experience A Weber Grillvorführung