GCSE(H),

To construct proportion equations from a description, first identify whether the relationship is a direct proportion or an indirect proportion.

Write the relationship as either `y prop x text( or ) y prop frac(1)(x)`.

Re-write the relationship as a formula:

`y = kx text( or ) y = k xx frac(1)(x)`

Substitute any initial values into the equation (normally this will be to work out the constant of proportionality).

Perform any remaining calculations to calculate additional values.

1. On one particular journey, the amount of fuel (*f*) used by a car was directly proportional to the distance (*d*) travelled. Over a distance of 100km, 2.5 litres of fuel was used. Find a formula for *f* in terms of *d*.

Answer: `f = 0.025d`

`f prop d`

`f = kd`

`2.5 = k xx 100`

`k = 2.5 รท 100 = 0.025`

Therefore `f = 0.025d`

2. Using the equation above, what distance was travelled on 5 litres of fuel?

Answer: 200km

Substituting into the equation: `5 = 0.025 xx d`

`d = 200`

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