5.5Mathematical Formulae

A formula is an equation that expresses the relationship between quantities. Given all variables except one, substitute the known values and solve for the unknown.

Finding an unknown in a formula

The formula for simple interest is $\displaystyle I = \frac{PRT}{100}$ . Find $\displaystyle T$ when $\displaystyle I = 540$ , $\displaystyle P = 3000$ and $\displaystyle R = 6$ .

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\displaystyle 540

\displaystyle = \frac{3000 \times 6 \times T}{100}

\displaystyle 540

\displaystyle = 180T

\displaystyle T

\displaystyle = 3

Now you try

The perimeter of a rectangle is $P = 2(l + w)$ . Find the value of $w$ when $P = 46$ and $l = 13$ .

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\displaystyle P

\displaystyle = 2(l + w) \quad \scriptsize\textit{substitute known values}

\displaystyle 46

\displaystyle = 2(13 + w)

\displaystyle \frac{46}{2}

\displaystyle = 13 + w \quad \scriptsize\textit{divide both sides by 2}

\displaystyle 23

\displaystyle = 13 + w

\displaystyle w

\displaystyle = 23 - 13

\displaystyle w

\displaystyle = 10

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