Work through the levels in order. Type your answer and press Check — open the worked solution if you get stuck. Answers like -6, 3/4 or 0.25 are typed exactly as shown. A ⭐ Bonus Challenge at the end is extra credit — skip it if the rest was hard work.
Level 1 · Warm-up
1 Sam earns $18 an hour. Last week he worked the hours shown. What was his gross pay?
Show worked solution
36 × $18 = $648. Overtime rate 1.5 × $18 = $27, and 3 × $27 = $81. Total $729. ($702 pays the overtime at the normal rate; $756 uses double time.)
2 $900 is invested at 7% p.a. simple interest for 2 years. Find the interest and the total amount at the end.
Show worked solution
I = 900 × 0.07 × 2 = $126. Total = 900 + 126 = $1026.
3 Leo is paid $20 an hour, and double time for every hour over 35 in a week. One week he earned $860. How many hours did he work that week?
Show worked solution
35 × $20 = $700. That leaves $160, and double time is $40 an hour, so 4 extra hours. 35 + 4 = 39 hours.
Level 2 · Core
4 A real-estate agent earns 2% commission on the first $500 000 of a sale price and 1% on the rest. She sells a house for $740 000. What is her commission?
Show worked solution
2% of $500 000 = $10 000. 1% of $240 000 = $2400. Total $12 400. ($14 800 charges 2% on everything; $7400 charges 1% on everything; $10 000 forgets the rest.)
5 What principal, invested at 4.5% p.a. simple interest, earns $360 of interest in 4 years?
Show worked solution
Each year earns 360 ÷ 4 = $90. If 0.045 × P = 90, then P = 90 ÷ 0.045 = $2000.
6 $2400 is invested at 3.5% p.a. simple interest. How many months does it take to earn $105 of interest?
Show worked solution
One year: 2400 × 0.035 = $84. 105 ÷ 84 = 1.25 years. 1.25 × 12 = 15 months.
Level 3 · Challenge
7 Ava is paid $26 an hour for 36 normal hours. The next 2 hours are at time-and-a-half, and any hours after that are double time. This week she worked 41 hours.1 Her overtime pay is $234.
2 Her total pay is $1170.
3 If all 5 overtime hours were at time-and-a-half, she would earn $26 less.
Which statements are correct?
2 Her total pay is $1170.
3 If all 5 overtime hours were at time-and-a-half, she would earn $26 less.
Which statements are correct?
Show worked solution
Overtime: 2 × $39 + 3 × $52 = $78 + $156 = $234 (1 ✓). Normal pay 36 × $26 = $936, total $1170 (2 ✓). 5 × $39 = $195, which is $39 less than $234, not $26 (3 ✗). 1 and 2.
8 Jo borrows some money at 4.8% p.a. simple interest for 30 months. She repays $1680 in total. How much did she borrow, and how much interest did she pay?
Show worked solution
N = 2.5, so I = 0.12 × P and the total is 1.12 × P = 1680. P = 1680 ÷ 1.12 = $1500, and I = 1680 − 1500 = $180. (Taking 12% of $1680 gives $201.60 — wrong, because the 12% is of the amount borrowed, not of the total.)
9 $1600 is invested at 6.25% p.a. simple interest. How many years does it take for the total amount to reach $3200?
Show worked solution
Interest needed: 3200 − 1600 = $1600. Each year: 1600 × 0.0625 = $100. 1600 ÷ 100 = 16 years.