Ratios & Rates
Simplify the ratio 18 : 24.
3 : 4
Find 15% of $60.
$9
Simplify: 3x + 5x − 2x
6x
x + 7 = 15
x = 8
A recipe uses flour and sugar in the ratio 5 : 2. If you use 350 g of flour, how much sugar do you need?
140 g
A jacket costs $120 and is discounted by 25%. What is the sale price?
$90
Expand and simplify: 2(x + 4) + 3x
5x + 8
3x = 27
x = 9
A car travels 270 km in 3 hours and 45 minutes. What is its speed in km/h?
72 km/h
A shop buys a watch for $80 and sells it for $100. What is the percentage profit?
25%
Substitute x = 3 into 4x² − 2x + 1.
31
x − 4 = −1
x = 3
Divide $480 in the ratio 3 : 5 : 8. How much is each share, and what is that as a percentage of the total?
$90 : $150 : $240
18.75% : 31.25% : 50%
A $250 item has 10% GST added. What is the final price, and how much GST is paid?
Final price: $275. GST: $25
Factorise fully: 6x² + 9x
3x(2x + 3)
x ÷ 5 = 7
x = 35