MAT-144 · Mathematical Reasoning Topic 02 · Conversions & Budgeting
Lesson 06 · Budgeting

Tell your money what to do.

A budget is a math instrument. It tells your dollars where to go before they vanish. Once you set it up in a spreadsheet, the percent and conversion tricks from this whole topic do the heavy lifting.

01Income vs. expenses 02Savings rate 03Set up MA1
▸ THE HOOK

Two weeks into the month, you check your bank account. The number is smaller than you expected. You know roughly where the money went: rent, groceries, gas, three Targets. But the math never quite lines up.

A budget closes that gap. It's not a punishment, it's a math instrument: income on top, fixed costs in the middle, what's left over on the bottom. Once you set it up, the percent and conversion tricks from the rest of Topic 2 do the heavy lifting.

A budget is a table that tells your money what to do.

Three parts that always add up: income (money in), expenses (money out, sliced into categories), and savings (what's left). Set it up once, change the numbers as life shifts, and the spreadsheet handles the recalc for you.
INCOME · $3,000 / MONTH WHERE IT GOES Rent · 30% Food · 15% Trans · 10% Other · 30% Save · 15% Same $3,000, sliced into categories. The slices ARE percent of income.

A real-world $3,000 monthly budget. The income bar splits into expense slices, with the teal-highlighted slice on the right being the savings.

▸ DEFINITION

A budget is a plan that allocates every dollar of income to either an expense category or to savings. Income = Expenses + Savings, always.

The vocabulary you'll see in word problems

  • Income Money coming in: paycheck, side hustle, gifts. Use take-home pay (after tax) for budgeting, not gross.
  • Expenses Money going out, broken into categories. Rent, food, transport, subscriptions, discretionary spending. Each category is a line item.
  • Fixed vs. variable Fixed expenses are the same every month (rent, phone bill, insurance). Variable expenses change (groceries, gas, eating out).
  • Savings rate Savings as a percent of income. savings / income × 100%. Higher is better. 10-20% is solid for an early-career budget.
  • Allocation The act of dividing income into expense categories and savings. A budget allocates every dollar to exactly one purpose — that's what makes a budget a budget rather than a guess. "Tell your money what to do."

Build a $3,000 monthly budget.

Five steps. Each one a small piece of the math you learned this week.

"Your take-home pay is $3,000 a month. Rent is $900, groceries average $450, transport (gas + transit) runs $300, and other expenses (utilities, phone, fun, subscriptions) total $900. What's your savings rate?"

1

Identify the income.

Take-home pay (after tax). For this budget, that's the $3,000 we have to allocate.

income = $3,000
2

List the expense categories.

Each category is a line item. Mix of fixed (rent) and variable (groceries, transport, other).

CategoryAmount% of income
Rent$90030%
Food$45015%
Transport$30010%
Other$90030%
3

Sum the expenses.

Add the four categories. This is the total monthly spend.

$900 + $450 + $300 + $900 = $2,550
4

Compute savings.

Savings is what's left after expenses.

$3,000 − $2,550 = $450
→ left over each month
5

Compute the savings rate.

Savings rate is savings as a percent of income. Same percent shape from Lesson 1: part / base, then × 100.

450 / 3,000 × 100 = 15%

Three problems. The same three moves.

Don't peek at the solutions. Each problem mirrors a real budgeting question.
PROBLEM 01 ☆ ☆   savings rate

Marco earns $2,500/month and spends $2,000/month. What's his savings rate? Type just the number (e.g. 20 for 20%).

savings rate =
PROBLEM 02 ★ ★ ☆   what's left

Jamie's monthly budget: income $3,200, rent $1,000, food $400, other $1,200. How many dollars are left for savings?

savings = $
PROBLEM 03 ★ ★ ★   percent budget

Ana spends 40% of her income on rent, 20% on food, and 25% on other expenses. What's her savings rate?

savings rate =

Three fast questions before you wrap.

Tap an answer.

Q1. Your monthly income is $2,400 and you save $360. Your savings rate is...

Why B? Savings rate = savings / income × 100. 360 / 2400 × 100 = 15%.

Q2. Which of these is a fixed expense?

Why C? Rent is the same every month (until your lease changes). The other three vary based on what you eat, how much you drive, etc.

Q3. If income is $X and total expenses are $Y, what's left for savings?

Why B? Savings is whatever's left after expenses come out: savings = income − expenses. The savings rate would be (X − Y) / X.
▸ TOPIC 02 · COMPLETE

Topic 2 in three moves.

You did it. Topic 2 is in the bag. The three moves you learned this week show up in adult life everywhere.

▸ Percent
L1, L2, L3
Out of 100. Convert to a decimal, then multiply or divide.
tip · tax · raise · discount · savings rate
▸ Conversions
L4, L5
Multiply by 1, in disguise. Set up so the unwanted unit cancels.
cooking · driving · currency · compound units
▸ Budget
L6
Income, expenses, savings. Tell your money what to do.
rent · food · transport · what's left to save

Your turn. Major Assignment 1 is a real budget you'll build in Excel. Pick a city, find rent prices, calculate take-home pay after taxes (percent), convert hourly to monthly (unit conversion), and end with a savings rate. Everything from this week, on one spreadsheet.

You've got this. The math is the easy part now.

{'num': '01', 'label': 'Percent fundamentals'} {'num': '02', 'label': 'Fractions, decimals, percents'} {'num': '03', 'label': 'Percent applications'} {'num': '04', 'label': 'Single conversions'} {'num': '05', 'label': 'Multi-step chains'} {'num': '06', 'label': 'Budgeting'}
Continue to Topic 03

Different angle? Need another rep? These are optional — tap any that look helpful.

▸ Browse all Topic 2 resources