Two quantities are in direct proportion when they increase at the same rate: double one and the other doubles. The cost of pens is proportional to the number of pens.
The unitary method finds the value of one first. If 7 pens cost $6.44, one pen costs 6.44 ÷ 7 = $0.92, so 6 pens cost 6 × 0.92 = $5.52. You can also write the relationship as y = kx, where k is the constant of proportionality, here 0.92.
Worked example
5 notebooks cost $23.45. How much do 3 notebooks cost?
- One notebook: 23.45 ÷ 5 = $4.69.
- Three notebooks: 3 × 4.69 = $14.07.
Answer:$14.07
Key words
- direct proportion
- both amounts change by the same factor
- unitary method
- find the value of one first
- constant of proportionality
- the number k in y = kx
Practise this
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Common Core-referenced: 7.RP.A.2