AI generatedRatio, proportion and rates of changeKS3 / GCSE

Comparing two direct-proportion models

A direct proportion model has the form with no fixed starting charge.

  • A direct proportion model has the form with no fixed starting charge.
  • For the same positive , the smaller positive constant gives the smaller .
  • Substitute the same input into both models, then compare in the same units.

Example 1

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 4 notebooks, and by how much?

Use the same number of notebooks.Use the same number of notebooks.
Shop A by £0.80

Example 2

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 5 notebooks, and by how much?

Use the same number of notebooks.Use the same number of notebooks.
Shop A by £1.50

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 6 notebooks, and by how much?

Check answer
Use the same number of notebooks.Use the same number of notebooks.
Shop A by £2.40
Question 2

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 7 notebooks, and by how much?

Check answer
Use the same number of notebooks.Use the same number of notebooks.
Shop A by £3.50
Question 3

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 8 notebooks, and by how much?

Check answer
Use the same number of notebooks.Use the same number of notebooks.
Shop A by £1.60
Question 4

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 9 notebooks, and by how much?

Check answer
Use the same number of notebooks.Use the same number of notebooks.
Shop A by £2.70
Question 5

Shop A charges pounds for notebooks. Shop B charges . Both have no delivery charge. Which costs less for 10 notebooks, and by how much?

Check answer
Use the same number of notebooks.Use the same number of notebooks.
Shop A by £4.00
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