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