Mathematics Standard • Year 12 • Ratios and rates • Lesson 2
Ratios in Context
Apply the three-step method to recipes, mixes, shared costs and map scales, where the ratio is described in words rather than handed to you.
1. Recipes and mixes
Show your working. 3 marks each
Q1.1 A biscuit dough uses flour and sugar in the ratio 5:3 and weighs 800 g in total. Find the mass of each.
Q1.2 A paint mix uses blue and yellow in the ratio 3:2. A painter uses 15 L of blue. How much yellow is needed, and what is the total volume?
2. Sharing by contribution
The ratio has to be built from the information first. 4 marks
Q2.1 Two partners invest $3000 and $4500 in a stall, which makes $1800 profit shared in the ratio of their investments. (a) Write the investment ratio in simplest form. (b) Find the two shares.
3. Map scales
A scale is a ratio between a map distance and a real distance. 2 marks
Q3.1 A map has a scale of 1:25 000. Two towns are 4 cm apart on the map. Find the real distance in kilometres.
How did this worksheet feel?
What I'll revisit before next class:
Q1.1, Flour and sugar
parts = 5 + 3 = 8, one part = 800 ÷ 8 = 100 g. Flour 500 g, sugar 300 g. Check: 500 + 300 = 800 g.
Q1.2, Paint mix
Blue is 3 parts, so one part = 15 ÷ 3 = 5 L. Yellow = 2 × 5 = 10 L, total 25 L. Check: 15 + 10 = 25.
Q2.1 (a), Investment ratio
3000:4500, HCF 1500, so 2:3.
Q2.1 (b), Profit shares
parts = 5, one part = 1800 ÷ 5 = $360. Shares $720 and $1080. Check: 720 + 1080 = 1800.
Q3.1, Map scale
4 × 25 000 = 100 000 cm = 1000 m = 1 km.