Budgeting and applications
Apply percentage increase and decrease to prices and incomes; analyse budget scenarios; solve multi-step financial problems involving saving and spending.
Worked examples
Calculating a percentage increase
Straightforward
Problem
A backpack costs and the price increases by . What is the new price?
1
Find the amount of the increase by calculating of the original price.
\text{Increase} = $95 \times 0.20 = $19.00
2
Add the increase to the original price to get the new price.
\text{New price} = $95 + $19 = $114.00
Answer
Analysing a budget
Moderate
Problem
Hannah earns per week. She spends on rent, on food, and on transport. How much does she have left each week for other expenses and savings?
1
Add the percentages for the three spending categories.
35\% + 20\% + 10\% = 65\%
2
Find the remaining percentage.
100\% - 65\% = 35\%
3
Calculate of Hannah's weekly income.
$1\,600 \times 0.35 = $560.00
Answer
per week
Saving toward a goal
Challenging
Problem
Ben earns per month and receives a pay rise. After the rise, he saves of his new monthly income. How much does Ben save in total over months?
1
Calculate Ben's new monthly income after the pay rise.
\text{New income} = $4\,000 \times 1.05 = $4\,200.00
2
Calculate his monthly savings as of the new income.
\text{Monthly savings} = $4\,200 \times 0.20 = $840.00
3
Multiply the monthly savings by to find total savings over a year.
\text{Total savings} = $840 \times 12 = $10\,080.00
Answer
Practise
Q1·Straightforward
A jacket costs and the price increases by . What is the new price?
Explanation
Increase . New price
Q2·Straightforward
A pair of shoes originally costs and is discounted by . What is the sale price?
Explanation
Discount . Sale price
Q3·Straightforward
Lia's annual salary is . She receives a pay rise. What is her new annual salary?
Explanation
Increase . New salary
Q4·Straightforward
A phone originally costs and is discounted by . What is the sale price?
Explanation
Discount . Sale price
Q5·Moderate
Sam earns per week and pays per week in rent. What percentage of his weekly income is spent on rent? Give your answer to 2 decimal places.
Explanation
Q6·Moderate
Emma's weekly budget is . She allocates to food, to rent, and to transport. How much money remains after these three categories?
Explanation
Total allocated . Remaining . Amount remaining
Q7·Moderate
A family's monthly grocery bill is . Due to price rises, the bill increases by . What is the new monthly grocery bill?
Explanation
Increase . New bill
Q8·Moderate
Alex's monthly budget for all expenses is . He spends on rent. What percentage of his monthly budget is spent on rent?
Explanation
Q9·Challenging
Kate saves per month for months, then receives a one-off bonus of . She wants to buy a laptop that costs . How much more does she still need to save after the 18 months and the bonus?
Explanation
Monthly savings . Total with bonus . Still needed
Q10·Challenging
Jake earns per year. He budgets for housing, for food, for transport, and for entertainment. How much is left per year for savings?
Explanation
Total allocated . Remaining . Savings
Q11·Challenging
Sam earns per month and receives a pay rise. After the rise, he decides to save of his new monthly income. How much does he save per month?
Explanation
New income . Monthly savings
Q12·Challenging
Priya is saving for a computer. She has already saved and can save per month. After more months of saving, how much more does she still need?
Explanation
Savings after 12 months . Still needed
Open Math
Budgeting and applications
Number and Algebra · MA5-NAF-C-01
Name:
Date:
Q1Straightforward
A jacket costs and the price increases by . What is the new price?
Q2Straightforward
A pair of shoes originally costs and is discounted by . What is the sale price?
Q3Straightforward
Lia's annual salary is . She receives a pay rise. What is her new annual salary?
Q4Straightforward
A phone originally costs and is discounted by . What is the sale price?
Q5Moderate
Sam earns per week and pays per week in rent. What percentage of his weekly income is spent on rent? Give your answer to 2 decimal places.
Q6Moderate
Emma's weekly budget is . She allocates to food, to rent, and to transport. How much money remains after these three categories?
Q7Moderate
A family's monthly grocery bill is . Due to price rises, the bill increases by . What is the new monthly grocery bill?
Q8Moderate
Alex's monthly budget for all expenses is . He spends on rent. What percentage of his monthly budget is spent on rent?
Q9Challenging
Kate saves per month for months, then receives a one-off bonus of . She wants to buy a laptop that costs . How much more does she still need to save after the 18 months and the bonus?
Q10Challenging
Jake earns per year. He budgets for housing, for food, for transport, and for entertainment. How much is left per year for savings?
Q11Challenging
Sam earns per month and receives a pay rise. After the rise, he decides to save of his new monthly income. How much does he save per month?
Q12Challenging
Priya is saving for a computer. She has already saved and can save per month. After more months of saving, how much more does she still need?
Worked solutions and answers at openmath.au/year-9/financial-mathematics/budgeting-and-applications