PROBLEM SOLVING WITH RATES

Students will be able to : • Make links between rates and ratios, and direct proportion• Simplify rates to solve problems

Review:

What is an example of a rate? A ratio?

What do rates and ratios have in common?

What is a difference between a rate and a ratio?

Does working with rates rely on direct proportion? Why?

Does working with ratios rely on direct proportion? Why?

Problem Solving Questions

Jenny bought a 45 g bag of lollies at the movies for $2.70.

a) How much would an 80 g bag of lollies cost?

b) How many grams of lollies could be bought for 65c?

Jenny bought a 45 g bag of lollies at the movies for $2.70.a) How much would an 80 g bag of lollies cost?b) How many grams of lollies could be bought for 65c?

Ask yourself these questions:

What are the two variables? (mass and cost) How do you know? (the units give that information)

Is this an example of direct proportion? (yes) How do you know? (as the amount of lollies bought increases, so too would the cost — and vice versa, in the same proportion — making it direct proportion)

What is the simplest cost per mass rate that we could write? ($2.70 ÷ 45 g = $0.06/g)

What is the simplest mass per cost rate that we could write? (45 g ÷ $2.70 = 16.7 g/$)

What other units could we use to understand this rate better? (e.g. 6c/g)

What do you need to consider about the units in order to answer part b) of the problem? (the units are not consistent — you need to use either c/g rate units or change the 65c into dollars to match the rate unit $/g)

Prices aren’t always directly proportional to the number of items. Which of these are in direct proportion?

a) A4 lecture pads (140 pages) cost $2.65 and 10 A4 lecture pads (140 pages) cost $26.50

b) An electronic game costs $29.95 and three games cost $89.

c) White enamel paint at $42.80 for five litres and $32.20 for four litres.

d) Downloading a song costs $0.99 and downloading five songs costs $4.95.

e) A 1 500 L water tank sells for $494 and a 2 500 L tank sells for $599.

f) A six-pack of socks cost $10.94 and a three-pack costs $5.47.